### Review Exercises

##### Understand Percent

In the following exercises, write each percent as a ratio.

$\text{53.3\%}$ rate of college students with student loans

In the following exercises, write as a ratio and then as a percent.

$9$ out of every $100$ nurses are men.

In the following exercises, convert each percent to a fraction.

$\text{175\%}$

$8\frac{1}{4}\%$

In the following exercises, convert each percent to a decimal.

$\text{23\%}$

4.9%

In the following exercises, convert each percent to ⓐ a simplified fraction and ⓑ a decimal.

In $2012,\text{13.5\%}$ of the United States population was age $65$ or over. (Source: www.census.gov)

In $2012,\text{6.5\%}$ of the United States population was under $5$ years old. (Source: www.census.gov)

When a die is tossed, the probability it will land with an even number of dots on the top side is $\text{50\%}.$

A couple plans to have three children. The probability they will all be girls is $\text{12.5\%}.$

In the following exercises, convert each decimal to a percent.

$0.15$

$3$

$1.395$

In the following exercises, convert each fraction to a percent.

$\frac{11}{5}$

$\frac{2}{9}$

According to the Centers for Disease Control, $\frac{2}{5}$ of adults do not take a vitamin or supplement.

According to the Centers for Disease Control, among adults who do take a vitamin or supplement, $\frac{3}{4}$ take a multivitamin.

In the following exercises, translate and solve.

$\text{120\%}$ of $55$ is what number?

$15$ is $\text{8\%}$ of what number?

$\text{7.9\%}$ of what number is $\text{\$4.74}?$

What percent of $340$ is $595?$

##### Solve General Applications of Percents

In the following exercises, solve.

When Aurelio and his family ate dinner at a restaurant, the bill was $\text{\$83.50}.$ Aurelio wants to leave $\text{20\%}$ of the total bill as a tip. How much should the tip be?

One granola bar has $2$ grams of fiber, which is $\text{8\%}$ of the recommended daily amount. What is the total recommended daily amount of fiber?

The nutrition label on a package of granola bars says that each granola bar has $190$ calories, and $54$ calories are from fat. What percent of the total calories is from fat?

Elsa gets paid $\text{\$4,600}$ per month. Her car payment is $\text{\$253}.$ What percent of her monthly pay goes to her car payment?

In the following exercises, solve.

Jorge got a raise in his hourly pay, from $\text{\$19.00}$ to $\text{\$19.76}.$ Find the percent increase.

Last year Bernard bought a new car for $\text{\$30,000}.$ This year the car is worth $\text{\$24,000}.$ Find the percent decrease.

##### Solve Sales Tax, Commission, and Discount Applications

In the following exercises, find ⓐ the sales tax ⓑ the total cost.

The cost of a lawn mower was $\text{\$750}.$ The sales tax rate is $\text{6\%}$ of the purchase price.

The cost of a water heater is $\text{\$577}.$ The sales tax rate is $\text{8.75\%}$ of the purchase price.

In the following exercises, find the sales tax rate.

Nahomi bought a purse for $\text{\$200}.$ The sales tax on the purchase was $\text{\$16.75}.$

In the following exercises, find the commission.

Ginny is a realtor. She receives $\text{3\%}$ commission when she sells a house. How much commission will she receive for selling a house for $\text{\$380,000}?$

Jackson receives $\text{16.5\%}$ commission when he sells a dinette set. How much commission will he receive for selling a dinette set for $\text{\$895}?$

In the following exercises, find the rate of commission.

Ruben received $\text{\$675}$ commission when he sold a $\text{\$4,500}$ painting at the art gallery where he works. What was the rate of commission?

Tori received $\text{\$80.75}$ for selling a $\text{\$950}$ membership at her gym. What was her rate of commission?

In the following exercises, find the sale price.

Aya bought a pair of shoes that was on sale for $\text{\$30}$ off. The original price of the shoes was $\text{\$75}.$

Takwanna saw a cookware set she liked on sale for $\text{\$145}$ off. The original price of the cookware was $\text{\$312}.$

In the following exercises, find ⓐ the amount of discount and ⓑ the sale price.

Nga bought a microwave for her office. The microwave was discounted $\text{30\%}$ from an original price of $\text{\$84.90}.$

Jarrett bought a tie that was discounted $\text{65\%}$ from an original price of $\text{\$45}.$

In the following exercises, find ⓐ the amount of discount ⓑ the discount rate. (Round to the nearest tenth of a percent if needed.)

Hilda bought a bedspread on sale for $\text{\$37}.$ The original price of the bedspread was $\text{\$50}.$

Tyler bought a phone on sale for $\text{\$49.99}.$ The original price of the phone was $\text{\$79.99}.$

In the following exercises, find

- ⓐ the amount of the mark-up
- ⓑ the list price

Manny paid $\text{\$0.80}$ a pound for apples. He added $\text{60\%}$ mark-up before selling them at his produce stand. What price did he charge for the apples?

It cost Noelle $\text{\$17.40}$ for the materials she used to make a purse. She added a $\text{325\%}$ mark-up before selling it at her friend’s store. What price did she ask for the purse?

##### Solve Simple Interest Applications

In the following exercises, solve the simple interest problem.

Find the simple interest earned after $4$ years on $\text{\$2,250}$ invested at an interest rate of $\text{5\%}.$

Find the simple interest earned after $7$ years on $\text{\$12,000}$ invested at an interest rate of $\text{8.5\%}.$

Find the principal invested if $\text{\$660}$ interest was earned in $5$ years at an interest rate of $\text{3\%}.$

Find the interest rate if $\text{\$2,898}$ interest was earned from a principal of $\text{\$23,000}$ invested for $3$ years.

Kazuo deposited $\text{\$10,000}$ in a bank account with interest rate $\text{4.5\%}.$ How much interest was earned in $2$ years?

Brent invested $\text{\$23,000}$ in a friend’s business. In $5$ years the friend paid him the $\text{\$23,000}$ plus $\text{\$9,200}$ interest. What was the rate of interest?

Fresia lent her son $\text{\$5,000}$ for college expenses. Three years later he repaid her the $\text{\$5,000}$ plus $\text{\$375}$ interest. What was the rate of interest?

In $6$ years, a bond that paid $\text{5.5\%}$ earned $\text{\$594}$ interest. What was the principal of the bond?

##### Solve Proportions and their Applications

In the following exercises, write each sentence as a proportion.

$95$ miles to $3$ gallons is the same as $475$ miles to $15$ gallons.

$\text{\$7.35}$ for $15$ ounces is the same as $\text{\$2.94}$ for $6$ ounces.

In the following exercises, determine whether each equation is a proportion.

$\frac{16}{7}=\frac{48}{23}$

$\frac{11.6}{9.2}=\frac{37.12}{29.44}$

In the following exercises, solve each proportion.

$\frac{7}{a}=\frac{\mathrm{-6}}{84}$

$\frac{\frac{1}{2}}{2}=\frac{m}{20}$

In the following exercises, solve the proportion problem.

The children’s dosage of acetaminophen is $5$ milliliters (ml) for every $25$ pounds of a child’s weight. How many milliliters of acetaminophen will be prescribed for a $60$ pound child?

After a workout, Dennis takes his pulse for $10$ sec and counts $21$ beats. How many beats per minute is this?

An $8$ ounce serving of ice cream has $272$ calories. If Lavonne eats $10$ ounces of ice cream, how many calories does she get?

Alma is going to Europe and wants to exchange $\text{\$1,200}$ into Euros. If each dollar is $0.75$ Euros, how many Euros will Alma get?

Zack wants to drive from Omaha to Denver, a distance of $494$ miles. If his car gets $38$ miles to the gallon, how many gallons of gas will Zack need to get to Denver?

Teresa is planning a party for $100$ people. Each gallon of punch will serve $18$ people. How many gallons of punch will she need?

In the following exercises, translate to a proportion.

$42$ is $\text{70\%}$ of what number?

What percent of $140$ is $210?$

In the following exercises, translate and solve using proportions.

$\text{6\%}$ of what number is $\text{\$24}?$

What percent of $\mathrm{3,100}$ is $930?$