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

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Question

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

Answer

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 $\small 25$ .

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Question

240 is 30% of what number?

Answer

Set up the proportion statement and solve for :

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

Cross-multiply:

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

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

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Question

420 is 150% of what number?

Answer

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

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

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

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

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Question

How much would a product sold for off cost?

Answer

First, find of :

$0.1\cdot $110=$11$

Then, subtract this value from the whole:

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Question

How much would a product sold for off cost?

Answer

First, find of :

$0.2\cdot $30=$6$

Then, subtract this value from the whole:

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Question

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

Answer

First, find of :

$0.4\cdot $500=$200$

Then, subtract this value from the whole:

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Question

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

Answer

First, multiply:

$35\ast .35=12.25$

Then subtract that amount from the original price:

Answer: The sale price is .

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Question

What is the sale price of a carton of milk if it is % off the original price of ?

Answer

First, multiply:

$3.20\ast .10=.32$

Then subtract that amount from the original price:

Answer: The sale price is .

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Question

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

Answer

First, multiply:

$90.00\ast .45=40.50$

Then subtract that amount from the original price:

Answer: The sale price is .

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Question

What is the sale price of a television if it is on sale for % off the original price of

Answer

First, multiply:

$175.00\ast .70=122.50$

Then subtract that amount from the original price:

Answer: The sale price is .

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Question

6 decreased by what percent is $4\frac{2}{3}$ ?

Select the closest answer.

Answer

The difference of 6 and $4\frac{2}{3}$ is

$6 - 4\frac{2}{3}$

$= \frac{6 \times 3}{3} - \frac{4 \times 3+ 2}{3}$

$= \frac{18}{3} - \frac{14}{3}$

$= \frac{18-14}{3}$

$= \frac{ 4}{3}$ .

Therefore, 6 is being decreased by $\frac{ 4}{3}$ ; to find out what percent this is of 6, we calculate:

$\frac{\frac{ 4}{3}}{6} \times 100 %$

$=\left ( \frac{ 4}{3} \div 6 \right ) \times 100 %$

$=\left ( \frac{ 4}{3} \times \frac{1}{6} \right ) \times 100 %$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}%$

$=\left ( \frac{ 2}{3} \times \frac{1}{3} \right ) \times \frac{100 }{1}%$

$=\left ( \frac{ 2 \times 1 \times 100}{3 \times 3 \times 1} \right ) %$

$= \frac{ 2 00}{9} %$

$2 00 \div 9 = 22 \textup{ R 2}$ , so

$\frac{ 2 00}{9} % = 22\frac{ 2 }{9} %$ .

The answer that comes closest among the four choices is 20%.

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Question

What number increased by 25% is equal to 7?

Answer

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

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

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Question

What number decreased by 25% is equal to 7?

Answer

To decrease a number by 25% is to take

of the number, or, equivalently, multiply it by

$\frac{75}{100} = \frac{75 \div 25 }{100 \div 25 } = \frac{3}{4}$ .

Therefore, we divide 7 by $\frac{3}{4}$ :

$7 \div \frac{3}{4} = \frac{7 }{1}\div \frac{3}{4} = \frac{7 }{1}\times \frac{4} {3}= \frac{7\times 4 }{1\times 3} = \frac{28}{3}$

$28 \div 3 = 9 \textup{ R }1$ , so

$\frac{28}{3} = 9 \frac{1}{3}$ .

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Question

What is the percentage of male students in a class if are male out of students?

Answer

First you want to make a proportion so $\frac{15}{20}$ of the class are male.

You can reduce this fraction by since both the numerator and denominator are divisible by it.

This gives you $\frac{3}{4}$ which as a decimal is .

To make that into a percentage, you multiple by and add a "%" symbol.

So that gives you .

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Question

is 30% of ; is 42% of .

is what percent of ?

Answer

We can choose a specific value for ; the reasoning is independent of this value.

Assume . Then

$A = 100 \cdot 30 % = 100 \cdot \frac{30}{100} = 30$

and

$B = 100 \cdot 42 % = 100 \cdot \frac{42}{100} = 42$

To find out what percent is of , calculate:

$\frac{B}{A} \times 100 % = \frac{42}{30} \times 100 % = 140 %$

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Question

If you get a 25% discount, what percentage of the original price will you have to pay?

Answer

The original price will represent 100% of the item price since that represents the whole for the problem.

If you get 25% off, you must take that away from the 100%.

so you will have to pay 75% of the original price.

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Question

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

Answer

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:

$15%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}38\ \times\ .15\end{array}}{ \ \ \ \space 5.70}$

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

$\frac{\begin{array}[b]{r}38.00\ -\ 5.70\end{array}}{ \ \ \ \space 32.30}$

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Question

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

Answer

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:

$15%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}41\ \times\ .15\end{array}}{ \ \ \ \space 6.15}$

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

$\frac{\begin{array}[b]{r}41.00\ -\ 6.15\end{array}}{ \ \ \ \space 34.85}$

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Question

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

Answer

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:

$15%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}22\ \times\ .15\end{array}}{ \ \ \ \space 3.30}$

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

$\frac{\begin{array}[b]{r}22.00\ -\ 3.30\end{array}}{ \ \ \ \space 18.70}$

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Question

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

Answer

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:

$15%\rightarrow0.15$

Next, we can multiply:

$\frac{\begin{array}[b]{r}15\ \times\ .15\end{array}}{ \ \ \ \space 2.25}$

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

$\frac{\begin{array}[b]{r}15.00\ -\ 2.25\end{array}}{ \ \ \space 12.75}$

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