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Common Core: 6th Grade Math : Solve Unit Rate Problems: CCSS.Math.Content.6.RP.A.3b

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Example Questions

Example Question #43 : Ratios & Proportional Relationships

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has $\displaystyle 9$ ears of corn, then how many turnips can he get?

Possible Answers:

$43\ \text{turnips}$ $\displaystyle 43\ \text{turnips}$

$93\ \text{turnips}$ $\displaystyle 93\ \text{turnips}$

$22\ \text{turnips}$ $\displaystyle 22\ \text{turnips}$

$94\ \text{turnips}$ $\displaystyle 94\ \text{turnips}$

$39\ \text{turnips}$ $\displaystyle 39\ \text{turnips}$

Correct answer:

$39\ \text{turnips}$ $\displaystyle 39\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 9$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{9\ \text{corn}}{T}$ $\displaystyle \frac{9\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{9\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{9\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$9\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 9\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=117 $\displaystyle 3T=117$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{117}{3}$ $\displaystyle \frac{3T}{3}=\frac{117}{3}$

Solve.

T=39 $\displaystyle T=39$

The farmer can get $39\ \text{turnips}$ $\displaystyle 39\ \text{turnips}$.

Report an Error

Example Question #51 : Algebraic Concepts

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has $\displaystyle 27$ ears of corn, then how many turnips can he get?

Possible Answers:

$87\ \text{turnips}$ $\displaystyle 87\ \text{turnips}$

$171\ \text{turnips}$ $\displaystyle 171\ \text{turnips}$

$111\ \text{turnips}$ $\displaystyle 111\ \text{turnips}$

$117\ \text{turnips}$ $\displaystyle 117\ \text{turnips}$

$127\ \text{turnips}$ $\displaystyle 127\ \text{turnips}$

Correct answer:

$117\ \text{turnips}$ $\displaystyle 117\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 27$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{27\ \text{corn}}{T}$ $\displaystyle \frac{27\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{27\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{27\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$27\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 27\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=351 $\displaystyle 3T=351$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{351}{3}$ $\displaystyle \frac{3T}{3}=\frac{351}{3}$

Solve.

T=117 $\displaystyle T=117$

The farmer can get $117\ \text{turnips}$ $\displaystyle 117\ \text{turnips}$.

Report an Error

Example Question #1 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has $\displaystyle 6$ ears of corn, then how many turnips can he get?

Possible Answers:

$26\ \text{turnips}$ $\displaystyle 26\ \text{turnips}$

$12\ \text{turnips}$ $\displaystyle 12\ \text{turnips}$

$24\ \text{turnips}$ $\displaystyle 24\ \text{turnips}$

$21\ \text{turnips}$ $\displaystyle 21\ \text{turnips}$

$62\ \text{turnips}$ $\displaystyle 62\ \text{turnips}$

Correct answer:

$26\ \text{turnips}$ $\displaystyle 26\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 6$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{6\ \text{corn}}{T}$ $\displaystyle \frac{6\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{6\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{6\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$6\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 6\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=78 $\displaystyle 3T=78$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{78}{3}$ $\displaystyle \frac{3T}{3}=\frac{78}{3}$

Solve.

T=26 $\displaystyle T=26$

The farmer can get $26\ \text{turnips}$ $\displaystyle 26\ \text{turnips}$.

Report an Error

Example Question #2 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has $\displaystyle 12$ ears of corn, then how many turnips can he get?

Possible Answers:

$57\ \text{turnips}$ $\displaystyle 57\ \text{turnips}$

$52\ \text{turnips}$ $\displaystyle 52\ \text{turnips}$

$65\ \text{turnips}$ $\displaystyle 65\ \text{turnips}$

$56\ \text{turnips}$ $\displaystyle 56\ \text{turnips}$

$60\ \text{turnips}$ $\displaystyle 60\ \text{turnips}$

Correct answer:

$52\ \text{turnips}$ $\displaystyle 52\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 12$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{12\ \text{corn}}{T}$ $\displaystyle \frac{12\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{12\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{12\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$12\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 12\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=156 $\displaystyle 3T=156$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{156}{3}$ $\displaystyle \frac{3T}{3}=\frac{156}{3}$

Solve.

T=52 $\displaystyle T=52$

The farmer can get $52\ \text{turnips}$ $\displaystyle 52\ \text{turnips}$.

Report an Error

Example Question #3 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has 210 $\displaystyle 210$ ears of corn, then how many turnips can he get?

Possible Answers:

$980\ \text{turnips}$ $\displaystyle 980\ \text{turnips}$

$180\ \text{turnips}$ $\displaystyle 180\ \text{turnips}$

$2100\ \text{turnips}$ $\displaystyle 2100\ \text{turnips}$

$910\ \text{turnips}$ $\displaystyle 910\ \text{turnips}$

$1009\ \text{turnips}$ $\displaystyle 1009\ \text{turnips}$

Correct answer:

$910\ \text{turnips}$ $\displaystyle 910\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 210 $\displaystyle 210$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{210\ \text{corn}}{T}$ $\displaystyle \frac{210\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{210\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{210\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$210\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 210\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=2730 $\displaystyle 3T=2730$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{2730}{3}$ $\displaystyle \frac{3T}{3}=\frac{2730}{3}$

Solve.

T=910 $\displaystyle T=910$

The farmer can get $910\ \text{turnips}$ $\displaystyle 910\ \text{turnips}$.

Report an Error

Example Question #4 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has 150 $\displaystyle 150$ ears of corn, then how many turnips can he get?

Possible Answers:

$860\ \text{turnips}$ $\displaystyle 860\ \text{turnips}$

$750\ \text{turnips}$ $\displaystyle 750\ \text{turnips}$

$560\ \text{turnips}$ $\displaystyle 560\ \text{turnips}$

$650\ \text{turnips}$ $\displaystyle 650\ \text{turnips}$

$550\ \text{turnips}$ $\displaystyle 550\ \text{turnips}$

Correct answer:

$650\ \text{turnips}$ $\displaystyle 650\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 150 $\displaystyle 150$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{150\ \text{corn}}{T}$ $\displaystyle \frac{150\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{150\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{150\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$150\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 150\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1950 $\displaystyle 3T=1950$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{1950}{3}$ $\displaystyle \frac{3T}{3}=\frac{1950}{3}$

Solve.

T=650 $\displaystyle T=650$

The farmer can get $650\ \text{turnips}$ $\displaystyle 650\ \text{turnips}$.

Report an Error

Example Question #65 : Equations

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has 180 $\displaystyle 180$ ears of corn, then how many turnips can he get?

Possible Answers:

$870\ \text{turnips}$ $\displaystyle 870\ \text{turnips}$

$787\ \text{turnips}$ $\displaystyle 787\ \text{turnips}$

$878\ \text{turnips}$ $\displaystyle 878\ \text{turnips}$

$780\ \text{turnips}$ $\displaystyle 780\ \text{turnips}$

$877\ \text{turnips}$ $\displaystyle 877\ \text{turnips}$

Correct answer:

$780\ \text{turnips}$ $\displaystyle 780\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 180 $\displaystyle 180$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{180\ \text{corn}}{T}$ $\displaystyle \frac{180\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{180\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{180\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$180\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 180\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=2340 $\displaystyle 3T=2340$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{2340}{3}$ $\displaystyle \frac{3T}{3}=\frac{2340}{3}$

Solve.

T=780 $\displaystyle T=780$

The farmer can get $780\ \text{turnips}$ $\displaystyle 780\ \text{turnips}$.

Report an Error

Example Question #66 : Equations

Possible Answers:

$924\ \text{turnips}$ $\displaystyle 924\ \text{turnips}$

$249\ \text{turnips}$ $\displaystyle 249\ \text{turnips}$

$429\ \text{turnips}$ $\displaystyle 429\ \text{turnips}$

$449\ \text{turnips}$ $\displaystyle 449\ \text{turnips}$

$483\ \text{turnips}$ $\displaystyle 483\ \text{turnips}$

Correct answer:

$429\ \text{turnips}$ $\displaystyle 429\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 99$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{99\ \text{corn}}{T}$ $\displaystyle \frac{99\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{99\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{99\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$99\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 99\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=1287 $\displaystyle 3T=1287$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{1287}{3}$ $\displaystyle \frac{3T}{3}=\frac{1287}{3}$

Solve.

T=429 $\displaystyle T=429$

The farmer can get $429\ \text{turnips}$ $\displaystyle 429\ \text{turnips}$.

Report an Error

Example Question #67 : Equations

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has $\displaystyle 36$ ears of corn, then how many turnips can he get?

Possible Answers:

$156\ \text{turnips}$ $\displaystyle 156\ \text{turnips}$

$166\ \text{turnips}$ $\displaystyle 166\ \text{turnips}$

$516\ \text{turnips}$ $\displaystyle 516\ \text{turnips}$

$165\ \text{turnips}$ $\displaystyle 165\ \text{turnips}$

$159\ \text{turnips}$ $\displaystyle 159\ \text{turnips}$

Correct answer:

$156\ \text{turnips}$ $\displaystyle 156\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has $\displaystyle 36$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{36\ \text{corn}}{T}$ $\displaystyle \frac{36\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{36\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{36\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$36\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 36\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

3T=468 $\displaystyle 3T=468$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{468}{3}$ $\displaystyle \frac{3T}{3}=\frac{468}{3}$

Solve.

T=156 $\displaystyle T=156$

The farmer can get $156\ \text{turnips}$ $\displaystyle 156\ \text{turnips}$.

Report an Error

Example Question #5 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade $\displaystyle 13$ turnips for $\displaystyle 3$ ears of corn. If a man has 3000 $\displaystyle 3000$ ears of corn, then how many turnips can he get?

Possible Answers:

$33000\ \text{turnips}$ $\displaystyle 33000\ \text{turnips}$

$13000\ \text{turnips}$ $\displaystyle 13000\ \text{turnips}$

$13113\ \text{turnips}$ $\displaystyle 13113\ \text{turnips}$

$13013\ \text{turnips}$ $\displaystyle 13013\ \text{turnips}$

$31000\ \text{turnips}$ $\displaystyle 31000\ \text{turnips}$

Correct answer:

$13000\ \text{turnips}$ $\displaystyle 13000\ \text{turnips}$

Explanation:

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$ $\displaystyle A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$ $\displaystyle 3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has 3000 $\displaystyle 3000$ ears of corn. Create a ratio with the variable $\displaystyle T$ that represents how many turnips he can get.

$\frac{3000\ \text{corn}}{T}$ $\displaystyle \frac{3000\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{3000\ \text{corn}}{T}$ $\displaystyle \frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{3000\ \text{corn}}{T}$

Cross multiply and solve for $\displaystyle T$.

$3000\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$ $\displaystyle 3000\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

$\displaystyle 3T=39000$

Divide both sides of the equation by $\displaystyle 3$.

$\frac{3T}{3}=\frac{39000}{3}$ $\displaystyle \frac{3T}{3}=\frac{39000}{3}$

Solve.

T=13000 $\displaystyle T=13000$

The farmer can get $13000\ \text{turnips}$ $\displaystyle 13000\ \text{turnips}$.

Report an Error

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Common Core: 6th Grade Math : Solve Unit Rate Problems: CCSS.Math.Content.6.RP.A.3b

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #43 : Ratios & Proportional Relationships

Example Question #51 : Algebraic Concepts

Example Question #1 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

Example Question #2 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

Example Question #3 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

Example Question #4 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

Example Question #65 : Equations

Example Question #66 : Equations

Example Question #67 : Equations

Example Question #5 : Solve Unit Rate Problems: Ccss.Math.Content.6.Rp.A.3b

All Common Core: 6th Grade Math Resources

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