# GED Math : Proportions and Percentages

## Example Questions

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### Example Question #1 : Proportions And Percentages

At a party, there are 7 women with blonde hair, 9 women with brown hair, and 5 women with red hair. What is the proportion of women with blonde hair?     Explanation:

A proprotion is the number of a specific event (blonde women) divided by the total number of events (total number of women). ### Example Question #2 : Proportions And Percentages

Solve:      Explanation: ### Example Question #3 : Proportions And Percentages

Solve:      Explanation: ### Example Question #3 : Proportions And Percentages

A bag contains green marbles, red marbles, and blue marbles. What is the proportion of red marbles?     Explanation:

The proportion is equal to the number of specific events (red marbles) divided by the total number of events (sum of all colors). ### Example Question #4 : Proportions And Percentages

What is of ?     Explanation: ### Example Question #6 : Proportions And Percentages

Sherry deposits \$3,000 at 6% simple interest per year. How much will she have in this account after three years, assuming she does not make any withdrawals or deposits?     Explanation:

Use the simple interest formula with : This is the simple interest earned. Add it to the original principal: ### Example Question #5 : Proportions And Percentages

The ratio of students to instructors at a prestigious law school is 15:4. If the school employs 120 instructors, then how many students total must it limit itself to enrolling in order to maintain this student-instructor ratio?     Explanation:

Let be the maximum number of students admitted.

For the school to maintain a 15:4 student-teacher ratio with 120 instructors, the ratios and must be equal. Therefore, we solve the proportion statement for :   The maximum number of students it can admit is 450.

### Example Question #1 : Proportions And Percentages

The ratio of students to instructors at a prestigious medical school is 25:6. The school employs 90 instructors, and there will be 240 students returning. How many new students must it limit itself to admitting in order to continue to maintain this student-instructor ratio?     Explanation:

Let be the maximum number of students admitted overall.

For the school to maintain a 25:6 student-teacher ratio with 90 instructors, the ratios and must be equal. Therefore, we solve the proportion statement for :   Since 240 spots are already filled by returning students, the medical school can admit up to new students.

### Example Question #41 : Complex Operations

Which of the following statements follows from the statement ?     Explanation:

Two ratios are equivalent if and only if their cross-products are equal. We look for the proportion statement whose cross-products are and . Of the four choices, only fits this criterion, so it is the correct choice.

### Example Question #10 : Proportions And Percentages

Which of the following statements does not follow from the statement ?     Explanation:

From we can conclude the following: is true, because the cross-products of a proportion statement are true. is true, because if two ratios are equivalent, their reciprocals are equivalent. can be demonstrated to be true as follows:    The fourth statement is false:   , which contradicts the statement that .

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