Use Proportional Relationships to Solve Multistep Ratio and Percent Problems: CCSS.Math.Content.7.RP.A.3 - 7th Grade Math
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200 percent of what number is equal to the difference between 75 and 25?
200 percent of what number is equal to the difference between 75 and 25?
We must first start by finding the difference between
and
:

Next find the decimal equivalent of
%, which is done by dividing by
:

Now we divide
by
.

Our final answer is
, because when it is multiplied by
%, it equals the difference between
and
.
We must first start by finding the difference between and
:
Next find the decimal equivalent of %, which is done by dividing by
:
Now we divide by
.
Our final answer is , because when it is multiplied by
%, it equals the difference between
and
.
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240 is 30% of what number?
240 is 30% of what number?
Set up the proportion statement and solve for
:

Cross-multiply:



Set up the proportion statement and solve for :
Cross-multiply:
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420 is 150% of what number?
420 is 150% of what number?
Set up the proportion statement and solve for
by cross-multiplying:




Set up the proportion statement and solve for by cross-multiplying:
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How much would a
product sold for
off cost?
How much would a product sold for
off cost?
First, find
of
:

Then, subtract this value from the whole:

First, find of
:
Then, subtract this value from the whole:
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How much would a
product sold for
off cost?
How much would a product sold for
off cost?
First, find
of
:

Then, subtract this value from the whole:

First, find of
:
Then, subtract this value from the whole:
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What is the sale price of a product that costs
if the sale is
off the original price?
What is the sale price of a product that costs if the sale is
off the original price?
First, find
of
:

Then, subtract this value from the whole:

First, find of
:
Then, subtract this value from the whole:
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What is the sale price of a game if it is
% off the original price of
?
What is the sale price of a game if it is % off the original price of
?
First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is
.
First, multiply:
Then subtract that amount from the original price:
Answer: The sale price is .
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What is the sale price of a carton of milk if it is
% off the original price of
?
What is the sale price of a carton of milk if it is % off the original price of
?
First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is
.
First, multiply:
Then subtract that amount from the original price:
Answer: The sale price is .
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What is the sale price of a pair of shoes if it is
% off the original price of
?
What is the sale price of a pair of shoes if it is % off the original price of
?
First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is
.
First, multiply:
Then subtract that amount from the original price:
Answer: The sale price is .
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What is the sale price of a television if it is on sale for
% off the original price of 
What is the sale price of a television if it is on sale for % off the original price of
First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is
.
First, multiply:
Then subtract that amount from the original price:
Answer: The sale price is .
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6 decreased by what percent is
?
Select the closest answer.
6 decreased by what percent is ?
Select the closest answer.
The difference of 6 and
is




.
Therefore, 6 is being decreased by
; to find out what percent this is of 6, we calculate:







, so
.
The answer that comes closest among the four choices is 20%.
The difference of 6 and is
.
Therefore, 6 is being decreased by ; to find out what percent this is of 6, we calculate:
, so
.
The answer that comes closest among the four choices is 20%.
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What number increased by 25% is equal to 7?
What number increased by 25% is equal to 7?
To increase a number by 25% is to take
of the number, or, equivalently, multiply it by
.
Therefore, we divide 7 by
:

, so
.
To increase a number by 25% is to take
of the number, or, equivalently, multiply it by
.
Therefore, we divide 7 by :
, so
.
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What number decreased by 25% is equal to 7?
What number decreased by 25% is equal to 7?
To decrease a number by 25% is to take
of the number, or, equivalently, multiply it by
.
Therefore, we divide 7 by
:

, so
.
To decrease a number by 25% is to take
of the number, or, equivalently, multiply it by
.
Therefore, we divide 7 by :
, so
.
Compare your answer with the correct one above
What is the percentage of male students in a class if
are male out of
students?
What is the percentage of male students in a class if are male out of
students?
First you want to make a proportion so
of the class are male.
You can reduce this fraction by
since both the numerator and denominator are divisible by it.
This gives you
which as a decimal is
.
To make that into a percentage, you multiple by
and add a "%" symbol.
So that gives you
.
First you want to make a proportion so of the class are male.
You can reduce this fraction by since both the numerator and denominator are divisible by it.
This gives you 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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is 30% of
;
is 42% of
.
is what percent of
?
is 30% of
;
is 42% of
.
is what percent of
?
We can choose a specific value for
; the reasoning is independent of this value.
Assume
. Then

and

To find out what percent
is of
, calculate:

We can choose a specific value for ; the reasoning is independent of this value.
Assume . Then
and
To find out what percent is of
, calculate:
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If you get a 25% discount, what percentage of the original price will you have to pay?
If you get a 25% discount, what percentage of the original price will you have to pay?
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.
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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A sweater was originally
, but the department store is running a
off sale. What is the sale price of the sweater?
A sweater was originally , but the department store is running a
off sale. What is the sale price of the sweater?
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:

Next, we can multiply:
![\frac{\begin{array}[b]{r}38\ \times\ .15\end{array}}{ \ \ \ \space 5.70}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912228/gif.latex)
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}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912230/gif.latex)
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:
Next, we can multiply:
Remember, we are taking off the original price, which means we need to subtract.
Compare your answer with the correct one above
A sweater was originally
, but the department store is running a
off sale. What is the sale price of the sweater?
A sweater was originally , but the department store is running a
off sale. What is the sale price of the sweater?
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:

Next, we can multiply:
![\frac{\begin{array}[b]{r}41\ \times\ .15\end{array}}{ \ \ \ \space 6.15}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912270/gif.latex)
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}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912271/gif.latex)
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:
Next, we can multiply:
Remember, we are taking off the original price, which means we need to subtract.
Compare your answer with the correct one above
A sweater was originally
, but the department store is running a
off sale. What is the sale price of the sweater?
A sweater was originally , but the department store is running a
off sale. What is the sale price of the sweater?
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:

Next, we can multiply:
![\frac{\begin{array}[b]{r}22\ \times\ .15\end{array}}{ \ \ \ \space 3.30}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912307/gif.latex)
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}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912308/gif.latex)
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:
Next, we can multiply:
Remember, we are taking off the original price, which means we need to subtract.
Compare your answer with the correct one above
A sweater was originally
, but the department store is running a
off sale. What is the sale price of the sweater?
A sweater was originally , but the department store is running a
off sale. What is the sale price of the sweater?
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:

Next, we can multiply:
![\frac{\begin{array}[b]{r}15\ \times\ .15\end{array}}{ \ \ \ \space 2.25}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912360/gif.latex)
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}](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/912361/gif.latex)
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:
Next, we can multiply:
Remember, we are taking off the original price, which means we need to subtract.
Compare your answer with the correct one above