7th Grade Math - Use Proportional Relationships to Solve Multistep Ratio and Percent Problems: CCSS.Math.Content.7.RP.A.3

What number increased by 25% is equal to 7?

$5 \frac{3}{5}$

$5\frac{1}{4}$

$5\frac{5}{6}$

$4\frac{2}{3}$

Explanation

To increase a number by 25% is to take

of the number, or, equivalently, multiply it by

$\frac{125}{100} = \frac{125 \div 25 }{100 \div 25 } = \frac{5}{4}$ .

Therefore, we divide 7 by $\frac{5}{4}$ :

$7 \div \frac{5}{4} = \frac{7 }{1}\div \frac{5}{4} = \frac{7 }{1}\times \frac{4} {5}= \frac{7\times 4 }{1\times 5} = \frac{28}{5}$

$28 \div 5 = 5 \textup{ R }3$ , so

$\frac{28}{5} = 5 \frac{3}{5}$ .

A sweater was originally , but the department store is running a off sale. What is the sale price of the sweater?

Explanation

In order to solve this problem, we need to calculate of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

$10%\rightarrow0.10$

Next, we can multiply:

$\frac{\begin{array}[b]{r}27\ \times\ .10\end{array}}{ \ \ \ \space 2.70}$

Remember, we are taking off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}27.00\ -\ 2.70\end{array}}{ \ \ \space 24.30}$

What is the sale price of a product that costs if the sale is off the original price?

Explanation

First, find of :

$0.4\cdot $500=$200$

Then, subtract this value from the whole:

What is the sale price of a pair of shoes if it is % off the original price of ?

Explanation

First, multiply:

$90.00\ast .45=40.50$

Then subtract that amount from the original price:

Answer: The sale price is .

How much would a product sold for off cost?

Explanation

First, find of :

$0.2\cdot $30=$6$

Then, subtract this value from the whole:

240 is 30% of what number?

Explanation

Set up the proportion statement and solve for :

$\frac{240}{N}= \frac{30}{100}$

Cross-multiply:

$N\cdot 30 = 240\cdot 100 = 24,000$

$N\cdot 30 \div 30= 24,000 \div 30$

200 percent of what number is equal to the difference between 75 and 25?

$\small 25$

$\small 50$

$\small 20$

$\small 30$

$\small 200$

Explanation

We must first start by finding the difference between $\small 75$ and $\small 25$ :

$\small 75-25 = 50$

Next find the decimal equivalent of $\small 200$ %, which is done by dividing by $\small 100$ :

$\small 200/100 = 2$

Now we divide $\small 50$ by $\small 2$ .

$\small 50/2 = 25$

Our final answer is $\small 25$ , because when it is multiplied by $\small 200$ %, it equals the difference between $\small 75$ and $\small 25$ .

420 is 150% of what number?

Explanation

Set up the proportion statement and solve for by cross-multiplying:

$\frac{420}{N}= \frac{150}{100}$

$N \cdot 150 = 420 \cdot 100 = 42,000$

$N \cdot 150 \div 150 = 42,000 \div 150$

A sweater was originally , but the department store is running a off sale. What is the sale price of the sweater?

Explanation

We can convert a percent into a decimal by moving the decimal two places to the left:

$20%\rightarrow0.20$

Next, we can multiply:

$\frac{\begin{array}[b]{r}15\ \times\ .20\end{array}}{ \ \ \ \space 3.00}$

Remember, we are taking off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}15.00\ -\ 3.00\end{array}}{ \ \ \space 12.00}$

A sweater was originally , but the department store is running a off sale. What is the sale price of the sweater?

Explanation

We can convert a percent into a decimal by moving the decimal two places to the left:

$20%\rightarrow0.20$

Next, we can multiply:

$\frac{\begin{array}[b]{r}40\ \times\ .20\end{array}}{ \ \ \ \space 8.00}$

Remember, we are taking off the original price, which means we need to subtract.

$\frac{\begin{array}[b]{r}40.00\ -\ 8.00\end{array}}{ \ \ \space 32.00}$

Use Proportional Relationships to Solve Multistep Ratio and Percent Problems: CCSS.Math.Content.7.RP.A.3

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