GED Math : Proportions and Percentages

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #21 : Proportions And Percentages

To get on the ballot for the student body president at McKinley High School, a student must turn in a petition with the signatures of 8% of the students from each of the three classes - sophomore, junior, and senior. There are 429 sophomores, 355 juniors, and 322 seniors enrolled at McKinley.

Greg has a petition with the signatures of 35 sophomores, 30 juniors, and 24 seniors. Can he get on the ballot with the signatures he has, and if not, why not?

Possible Answers:

Greg has the signatures he needs to get on the ballot.

Greg cannot get on the ballot yet, because he needs more signatures from sophomores.

Greg cannot get on the ballot yet, because he needs more signatures from juniors.

Greg cannot get on the ballot yet, because he needs more signatures from seniors.

Correct answer:

Greg cannot get on the ballot yet, because he needs more signatures from seniors.

Explanation:

In order to answer the question, we must find out the percent of each class that has signed Greg's petition, and compare it to 8%.

 

Sophomores: 35 out of 429, which is  of the sophomores.

 

Juniors: 30 out of 355,which is  of the juniors.

 

Seniors: 24 out of 322, which is  of the seniors.

 

Greg has sufficient signatures from sophomores and juniors, but not seniors.

Example Question #22 : Proportions And Percentages

Menu

Above is the menu for a coffee shop. The shop charges 7% sales tax.

Clara orders two large iced coffees, one large cappucino, one large cafe latte, and four butter croissants. She hands the cashier a twenty-dollar bill and a ten-dollar bill. How much will Clara get back in change?

Possible Answers:

The amount Clara has paid is insufficient.

Correct answer:

Explanation:

Add up the pretax prices of Clara's items to find the total pretax amaount:

The tax is 7% of this, or

, rounded to the nearest cent.

Add the amounts to get the cost after tax:

Since Clara has paid $30, her change will be

Example Question #381 : Ged Math

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 6,988 students, how many signatures must a student get to be on that ballot?

Possible Answers:

Correct answer:

Explanation:

3% of a number is equal to that number multplied by 0.03, so 3% of the student population of 6,988 is 

.

Round this to the nearest whole number, which is 210 students.

Example Question #24 : Proportions And Percentages

A quantity of a 10% acid solution is mixed with twice as much of a 20% acid solution. 

Give the concentration, in percent, of acid in the resulting solution.

Possible Answers:

Correct answer:

Explanation:

Since the correct answer is independent of the actual amounts, for simplicity's sake, we will assume that 100 mL of the 10% solution was used. Then the amount of 20% solution used was twice this, or 200 mL. The total amount of solution is 300 mL.

100 mL of 10% acid solution contains  mL of acid.

200 mL of 20% acid solution contains  mL of acid.

This is a total of 50 mL of acid out of 300 mL of solution.Therefore, the concentration of acid in the final mixture is

.

Example Question #25 : Proportions And Percentages

Laura currently makes $9.50 an hour working 30 hours a week. She has been told by her boss that she is getting a raise in her wages to $11.25 a week, and that she will be working a 40-hour week. By what percent will her weekly earnings increase (nearest whole)?

Possible Answers:

Correct answer:

Explanation:

Laura currently makes 

 per week.

After her raise and her increase in work hours, she will make

 per week,

an increase of .

This is an increase of 

.

Example Question #26 : Proportions And Percentages

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 6,988 students, how many signatures must a student get to be on that ballot?

Possible Answers:

Correct answer:

Explanation:

3% of a number is equal to that number multplied by 0.03, so 3% of the student population of 6,988 is 

.

Round this to the nearest whole number, which is 210 students.

Example Question #27 : Proportions And Percentages

Lucy's weight increased from 180 pounds to 200 pounds. By what percent (nearest tenth, if applicable) did her weight increase?

Possible Answers:

Correct answer:

Explanation:

In a percent of increase problem, the whole is the amount at the beginning of the time period, which here is 180 pounds. The part is the difference between the final and initial amounts, which here is  pounds. To find what percent 20 is of 180, calculate:

Example Question #28 : Proportions And Percentages

To get on the ballot for the student body president at Parker High School, a student must turn in a petition with the signatures of 8% of the students from each of the three classes - sophomore, junior, and senior. There are 365 sophomores, 315 juniors, and 268 seniors enrolled at Parker.

Marisol has a petition with the signatures of 35 sophomores, 30 juniors, and 24 seniors. Can she get on the ballot with the signatures she has, and if not, why not?

Possible Answers:

Marisol cannot get on the ballot yet, because she needs more signatures from sophomores.

Marisol cannot get on the ballot yet, because she she needs more signatures from seniors.

Marisol has the signatures she needs to get on the ballot.

Marisol cannot get on the ballot yet, because she needs more signatures from juniors.

Correct answer:

Marisol has the signatures she needs to get on the ballot.

Explanation:

In order to answer the question, we must find out the percent of each class that has signed Marisol's petition, and compare it to 8%.

 

Sophomores: 35 out of 365, which is  of the sophomores.

 

Juniors: 30 out of 315, which is  of the juniors.

 

Seniors: 24 out of 268, which is  of the seniors.

 

Marisol has sufficient signatures from all three classs, and thus has the signatures she needs to get on the ballot.

Example Question #29 : Proportions And Percentages

Members of a grocery co-operative can earn a discount by working at the grocery; for every full hour they work over a given week, they can take 4% off of their grocery bill the next week.

Michael is a member of this co-operative. He wants to work enough hours so that he can purchase the groceries he needs, which normally would cost him $140, for at most $100. How many hours must he work, at the very least, in order to get this discount?

Possible Answers:

Correct answer:

Explanation:

Michael wants to save $40 on a $140, which is a discount of

.

Ha saves 4% per hour he works in the grocery, so if  is the number of hours he works in the grocery, he saves . He wants this to be at least 28.6%, so we can solve for  in the following inequality:

Since the discount is a function of a whole number of hours worked, Michael will need to work 8 hours to pay less than $100 for the groceries.

Example Question #30 : Proportions And Percentages

Thingy

Refer to the above diagram. The circles are of equal size and the portions of each circle are of equal size.

If the shaded portion of the circle at lower right were to be unshaded, then by what percent would the area of the unshaded region increase?

Possible Answers:

Correct answer:

Explanation:

At current, 5 regions of equal size are unshaded. If the remainder of the lower right circle were shaded, this would increase the size by 3 regions of the same size. Therefore, we need to calculate what percent 3 is of 5. This is an increase in area of

.

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