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Common Core: 7th Grade Math : Decide if Two Quantiies are in a Proportional Relationship: CCSS.Math.Content.7.RP.A.2a

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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Example Questions

Example Question #1 : Proportion / Ratio / Rate

In a class of $\displaystyle 60$ students, the ratio of freshmen to sophomores to juniors is 2:3:5 $\displaystyle 2:3:5$. How many juniors are in the class?

Possible Answers:

$\displaystyle 18$

$\displaystyle 12$

$\displaystyle 15$

$\displaystyle 30$

Correct answer:

$\displaystyle 30$

Explanation:

Let $\displaystyle 2x$ be the number of freshmen, $\displaystyle 3x$ be the number of sophomores, and $\displaystyle 5x$ be the number of juniors.

Now, since we have $\displaystyle 60$ students,

$\displaystyle 2x+3x+5x=60$

10x=60 $\displaystyle 10x=60$

x=6 $\displaystyle x=6$

Since we want to find the number of juniors, we need to find the value of $\displaystyle 5x$.

$\displaystyle 5x=5(6)=30$

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Example Question #81 : Ratios & Proportional Relationships

In a zoo with 200 $\displaystyle 200$ animals, the ratio of mammals to reptiles to birds is 5:6:9 $\displaystyle 5:6:9$. How many birds does the zoo have?

Possible Answers:

$\displaystyle 90$

100 $\displaystyle 100$

$\displaystyle 50$

$\displaystyle 60$

Correct answer:

$\displaystyle 90$

Explanation:

Let $\displaystyle 5x$ be the number of mammals,$\displaystyle 6x$ be the number of reptiles, and $\displaystyle 9x$ be the number of birds.

Since the zoo has 200 $\displaystyle 200$ animals,

$\displaystyle 5x+6x+9x=200$

20x=200 $\displaystyle 20x=200$

x=10 $\displaystyle x=10$

Because we want the number of birds, we need to find the value of $\displaystyle 9x$.

$\displaystyle 9x=9(10)=90$

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Example Question #2 : Proportion / Ratio / Rate

In a high school of 2000 $\displaystyle 2000$ students, the ratio of freshmen to sophomores to juniors to seniors is $\displaystyle 2:3:8:12$. How many juniors does this high school have?

Possible Answers:

800 $\displaystyle 800$

960 $\displaystyle 960$

500 $\displaystyle 500$

640 $\displaystyle 640$

Correct answer:

640 $\displaystyle 640$

Explanation:

Let $\displaystyle 2x$ be the number of freshmen, $\displaystyle 3x$ be the number of sophomores, $\displaystyle 8x$ be the number of juniors, and 12x $\displaystyle 12x$ be the number of seniors.

Because the high school has 2000 $\displaystyle 2000$ students,

$\displaystyle 2x+3x+8x+12x=2000$

$\displaystyle 25x=2000$

x=80 $\displaystyle x=80$

Since we want to find out how many juniors there are, we need the value of $\displaystyle 8x$.

$8x=80\times8=640$ $\displaystyle 8x=80\times8=640$

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Example Question #61 : Number Concepts And Operations

In a high school, the ratio of freshmen to seniors is 4:5 $\displaystyle 4:5$. If there are 150 $\displaystyle 150$ seniors, how many freshmen are there?

Possible Answers:

120 $\displaystyle 120$

110 $\displaystyle 110$

100 $\displaystyle 100$

180 $\displaystyle 180$

Correct answer:

120 $\displaystyle 120$

Explanation:

Set up the following proportion, with $\displaystyle x$ being the number of freshmen.

$\frac{4}{5}=\frac{x}{150}$ $\displaystyle \frac{4}{5}=\frac{x}{150}$

Now, cross-multiply and solve for $\displaystyle x$.

5x=600 $\displaystyle 5x=600$

x=120 $\displaystyle x=120$

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Example Question #3 : Proportion / Ratio / Rate

On a beach, the ratio of crabs to seagulls is 9:5 $\displaystyle 9:5$. If there are 182 $\displaystyle 182$ crabs and seagulls on the beach, how many crabs are there?

Possible Answers:

$\displaystyle 38$

109 $\displaystyle 109$

114 $\displaystyle 114$

117 $\displaystyle 117$

Correct answer:

117 $\displaystyle 117$

Explanation:

Let $\displaystyle 9x$ be the number of crabs and $\displaystyle 5x$ be the number of seagulls.

Since there are 182 $\displaystyle 182$ crabs and seagulls on the beach,

$\displaystyle 9x+5x=182$

14x=182 $\displaystyle 14x=182$

x=13 $\displaystyle x=13$

Because the question asks for the number of crabs, we need to find the value of $\displaystyle 9x$.

$9x=13\times9=117$ $\displaystyle 9x=13\times9=117$

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Example Question #1 : Fractions

There are $\displaystyle 45$ boys and $\displaystyle 36$ girls at a playground. What is the ratio of boys to girls?

Possible Answers:

5:4 $\displaystyle 5:4$

4:3 $\displaystyle 4:3$

4:5 $\displaystyle 4:5$

3:4 $\displaystyle 3:4$

Correct answer:

5:4 $\displaystyle 5:4$

Explanation:

Write the numbers of boys and girls as a fraction, then simplify.

$\frac{45}{36}=\frac{5}{4}$ $\displaystyle \frac{45}{36}=\frac{5}{4}$

$\frac{5}{4}$ $\displaystyle \frac{5}{4}$ can also be written as 5:4 $\displaystyle 5:4$

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Example Question #62 : Number Concepts And Operations

At a high school, there are $\displaystyle 36$ freshmen, $\displaystyle 42$ sophomores, $\displaystyle 24$ juniors, and $\displaystyle 30$ seniors. What is the ratio of seniors to freshmen?

Possible Answers:

$\displaystyle 5$ to $\displaystyle 6$

$\displaystyle 7$ to $\displaystyle 6$

$\displaystyle 6$ to $\displaystyle 5$

$\displaystyle 2$ to $\displaystyle 3$

Correct answer:

$\displaystyle 5$ to $\displaystyle 6$

Explanation:

Write the number of seniors and numbers of freshmen as a fraction:

$\frac{30}{36}=\frac{5}{6}$ $\displaystyle \frac{30}{36}=\frac{5}{6}$

That fraction is equivalent to $5\text{ to }6$ $\displaystyle 5\text{ to }6$.

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Example Question #4 : Proportion / Ratio / Rate

The angles in a triangle are in the ratio 1:3:6 $\displaystyle 1:3:6$. What is the angle measurement of the largest angle?

Possible Answers:

$100^{\circ}$ $\displaystyle 100^{\circ}$

$108^{\circ}$ $\displaystyle 108^{\circ}$

$98^{\circ}$ $\displaystyle 98^{\circ}$

$54^{\circ}$ $\displaystyle 54^{\circ}$

Correct answer:

$108^{\circ}$ $\displaystyle 108^{\circ}$

Explanation:

Let $x, 3x, \text{ and }6x$ $\displaystyle x, 3x, \text{ and }6x$ be the values of the angles.

Since all the angles in a triangle need to add up to 180 $\displaystyle 180$,

$\displaystyle x+3x+6x=180$

10x=180 $\displaystyle 10x=180$

x=18 $\displaystyle x=18$

Because we want the value of the largest angle, we need to find the value of $\displaystyle 6x$.

$\displaystyle 6x=18(6)=108$

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Example Question #14 : Fractions

John and Michela are business partners who agreed to split profits at a ratio of 2:3, with Michela taking the larger share. If their business made $\$36\textup{,}000$ $\displaystyle \$36\textup{,}000$ in the first year, how much money did Michela make?

Possible Answers:

$\$22\textup{,}200$ $\displaystyle \$22\textup{,}200$

$\$14\textup{,}400$ $\displaystyle \$14\textup{,}400$

$\$18\textup{,}600$ $\displaystyle \$18\textup{,}600$

$\$21\textup{,}600$ $\displaystyle \$21\textup{,}600$

Correct answer:

$\$21\textup{,}600$ $\displaystyle \$21\textup{,}600$

Explanation:

Let $\displaystyle 2x$ be the amount John takes home and $\displaystyle 3x$ be the amount Michela takes home.

Since their business made $\$36,000$ $\displaystyle \$36,000$,

$\displaystyle 2x+3x=36000$

$\displaystyle 5x=36000$

x=7200 $\displaystyle x=7200$

We want to know how much Michela made so we need to find the value of $\displaystyle 3x$.

$3x=7200\times3=21600$ $\displaystyle 3x=7200\times3=21600$

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Example Question #11 : Fractions

The angles in a triangle have a ratio of 3:4:5 $\displaystyle 3:4:5$. What is the measurement of the smallest angle?

Possible Answers:

$35^{\circ}$ $\displaystyle 35^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

$105^{\circ}$ $\displaystyle 105^{\circ}$

$55^{\circ}$ $\displaystyle 55^{\circ}$

Correct answer:

$45^{\circ}$ $\displaystyle 45^{\circ}$

Explanation:

Let $3x, 4x,\text{ and}, 5x$ $\displaystyle 3x, 4x,\text{ and}, 5x$ be the values of the angles.

Since there are 180 $\displaystyle 180$ degrees in a triangle,

$\displaystyle 3x+4x+5x=180$

12x=180 $\displaystyle 12x=180$

x=15 $\displaystyle x=15$

Since we want the value of the smallest angle, find the value of $\displaystyle 3x$.

$3x=15\times3=45$ $\displaystyle 3x=15\times3=45$

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Common Core: 7th Grade Math : Decide if Two Quantiies are in a Proportional Relationship: CCSS.Math.Content.7.RP.A.2a

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Proportion / Ratio / Rate

Example Question #81 : Ratios & Proportional Relationships

Example Question #2 : Proportion / Ratio / Rate

Example Question #61 : Number Concepts And Operations

Example Question #3 : Proportion / Ratio / Rate

Example Question #1 : Fractions

Example Question #62 : Number Concepts And Operations

Example Question #4 : Proportion / Ratio / Rate

Example Question #14 : Fractions

Example Question #11 : Fractions

All Common Core: 7th Grade Math Resources

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