ISEE Middle Level Math : How to find the whole from the part with percentage

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

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Example Question #1 : How To Find The Whole From The Part With Percentage

Pie_graph

Refer to the above diagram. If there were 15,934 voters who were affiliated with a political party in Smith County in 2009, how many voters (nearest whole number) were there total?

Possible Answers:

Correct answer:

Explanation:

40% of the voters were registered as independents, so 60% were registered as a member of a political party. Since 60% of the voters numbered 15,934, we can find the total number of voters by setting up and solving a proportion:

which rounds to 26,557 voters.

 

Example Question #2 : How To Find The Whole From The Part With Percentage

Pie_graph

Refer to the above graph. If there were 17,856 registered voters in Smith County in 2009, how many voters were registered as neither Republicans nor Democrats (nearest whole number)?

Possible Answers:

Correct answer:

Explanation:

2% of the voters were registered as members of other parties, and 40% were unaffiliated, so we want to calculate 42% of 17,856, or, equivalently, 

which, to the nearest whole number, rounds to 7,500 voters.

Example Question #7 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

240 is 30% of what number?

Possible Answers:

Correct answer:

Explanation:

Set up the proportion statement and solve for :

Cross-multiply:

Example Question #8 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

420 is 150% of what number?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #3 : How To Find The Whole From The Part With Percentage

70 is  of what number?

Possible Answers:

Correct answer:

Explanation:

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

Example Question #4 : How To Find The Whole From The Part With Percentage

24 is 25% of what number?

Possible Answers:

Correct answer:

Explanation:

Think is of .

 

So:

 

and .

 

We have:

 

 

Example Question #5 : How To Find The Whole From The Part With Percentage

Julie bought some groceries at the store where she works for $196.57. She got an employee discount of 15%. How much would the same groceries cost a non-employee?

Possible Answers:

Correct answer:

Explanation:

Paying at a 15% discount is equvalent to paying 85% of the original price, so $196.57 is 85% of the original (non-employee) price, or, equivalently, 0.85 times that price. If  is that price, then we can set up and solve the equation:

A non-employee would pay $231.26 for the groceries.

Example Question #6 : How To Find The Whole From The Part With Percentage

Becky ate  of a batch of cupcakes. She ate  cupcakes. How many cupcakes were there in total?

Possible Answers:

Correct answer:

Explanation:

This can be solved using a proportion:

Cross multiply and solve for :

Example Question #7 : How To Find The Whole From The Part With Percentage

For her birthday, Susan asks her mother to buy her a car. Susan’s mother agrees to give Susan 150 percent of whatever amount Susan can save up in six months. If Susan saves , how much does Susan’s mother owe her?

Possible Answers:

$700

$900

 

 

 

 

$750

$300

$550

Correct answer:

$900

 

 

 

 

Explanation:

When Susan's mother agreed to match her savings plus fifty percent, she agreed to give Susan % plus %.  

Before multiplying by the amount Susan saved, we must convert % to a decimal by dividing by .

Now we multiply time $.

Susan's mother owes her $.

Example Question #8 : How To Find The Whole From The Part With Percentage

If sales tax on a pair of jeans is , and the jeans cost  before tax, what is the final price of the jeans including tax?

Possible Answers:

$56

$60

$58

$66

$62

Correct answer:

$58

Explanation:

Since the jeans are the only item being purchased, and they cost $, we must first find % of $.  In order to do that we multiply $ by the decimal form of %, which is .

Note: In order to find the decimal form of a percent, we divide it by .  

Find the tax:

 

Therefore the sales tax added to the original price is $

The final cost of the jeans is $.

 

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