6.5 Solve Proportions and their Applications

$4$ is to $15$ as $36$ is to $135.$

$7$ is to $9$ as $35$ is to $45.$

$12$ is to $5$ as $96$ is to $40.$

$15$ is to $8$ as $75$ is to $40.$

$5$ wins in $7$ games is the same as $115$ wins in $161$ games.

$4$ wins in $9$ games is the same as $36$ wins in $81$ games.

$8$ campers to $1$ counselor is the same as $48$ campers to $6$ counselors.

$6$ campers to $1$ counselor is the same as $48$ campers to $8$ counselors.

$\text{\$9.36}$ for $18$ ounces is the same as $\text{\$2.60}$ for $5$ ounces.

$\text{\$3.92}$ for $8$ ounces is the same as $\text{\$1.47}$ for $3$ ounces.

$\text{\$18.04}$ for $11$ pounds is the same as $\text{\$4.92}$ for $3$ pounds.

$\text{\$12.42}$ for $27$ pounds is the same as $\text{\$5.52}$ for $12$ pounds.

$$\frac{7}{15}=\frac{56}{120}$$

$$\frac{5}{12}=\frac{45}{108}$$

$$\frac{11}{6}=\frac{21}{16}$$

$$\frac{9}{4}=\frac{39}{34}$$

$$\frac{12}{18}=\frac{4.99}{7.56}$$

$$\frac{9}{16}=\frac{2.16}{3.89}$$

$$\frac{13.5}{8.5}=\frac{31.05}{19.55}$$

$$\frac{10.1}{8.4}=\frac{3.03}{2.52}$$

$$\frac{x}{56}=\frac{7}{8}$$

$$\frac{n}{91}=\frac{8}{13}$$

$$\frac{49}{63}=\frac{z}{9}$$

$$\frac{56}{72}=\frac{y}{9}$$

$$\frac{5}{a}=\frac{65}{117}$$

$$\frac{4}{b}=\frac{64}{144}$$

$$\frac{98}{154}=\frac{\mathrm{-7}}{p}$$

$$\frac{72}{156}=\frac{\mathrm{-6}}{q}$$

$$\frac{a}{\mathrm{-8}}=\frac{\mathrm{-42}}{48}$$

$$\frac{b}{\mathrm{-7}}=\frac{\mathrm{-30}}{42}$$

$$\frac{2.6}{3.9}=\frac{c}{3}$$

$$\frac{2.7}{3.6}=\frac{d}{4}$$

$$\frac{2.7}{j}=\frac{0.9}{0.2}$$

$$\frac{2.8}{k}=\frac{2.1}{1.5}$$

$$\frac{\frac{1}{2}}{1}=\frac{m}{8}$$

$$\frac{\frac{1}{3}}{3}=\frac{9}{n}$$

Pediatricians prescribe $5$ milliliters (ml) of acetaminophen for every $25$ pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs $45$ pounds?

Brianna, who weighs $6$ kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at $15$ milligrams (mg) for every $1$ kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?

At the gym, Carol takes her pulse for $10$ sec and counts $19$ beats. How many beats per minute is this? Has Carol met her target heart rate of $140$ beats per minute?

Kevin wants to keep his heart rate at $160$ beats per minute while training. During his workout he counts $27$ beats in $10$ seconds. How many beats per minute is this? Has Kevin met his target heart rate?

A new energy drink advertises $106$ calories for $8$ ounces. How many calories are in $12$ ounces of the drink?

One $12$ ounce can of soda has $150$ calories. If Josiah drinks the big $32$ ounce size from the local mini-mart, how many calories does he get?

Karen eats $\frac{1}{2}$ cup of oatmeal that counts for $2$ points on her weight loss program. Her husband, Joe, can have $3$ points of oatmeal for breakfast. How much oatmeal can he have?

An oatmeal cookie recipe calls for $\frac{1}{2}$ cup of butter to make $4$ dozen cookies. Hilda needs to make $10$ dozen cookies for the bake sale. How many cups of butter will she need?

Janice is traveling to Canada and will change $\text{\$250}$ US dollars into Canadian dollars. At the current exchange rate, $\text{\$1}$ US is equal to $\text{\$1.01}$ Canadian. How many Canadian dollars will she get for her trip?

Todd is traveling to Mexico and needs to exchange $\text{\$450}$ into Mexican pesos. If each dollar is worth $12.29$ pesos, how many pesos will he get for his trip?

Steve changed $\text{\$600}$ into $480$ Euros. How many Euros did he receive per US dollar?

Martha changed $\text{\$350}$ US into $385$ Australian dollars. How many Australian dollars did she receive per US dollar?

At the laundromat, Lucy changed $\text{\$12.00}$ into quarters. How many quarters did she get?

When she arrived at a casino, Gerty changed $\text{\$20}$ into nickels. How many nickels did she get?

Jesse’s car gets $30$ miles per gallon of gas. If Las Vegas is $285$ miles away, how many gallons of gas are needed to get there and then home? If gas is $\text{\$3.09}$ per gallon, what is the total cost of the gas for the trip?

Danny wants to drive to Phoenix to see his grandfather. Phoenix is $370$ miles from Danny’s home and his car gets $18.5$ miles per gallon. How many gallons of gas will Danny need to get to and from Phoenix? If gas is $\text{\$3.19}$ per gallon, what is the total cost for the gas to drive to see his grandfather?

Hugh leaves early one morning to drive from his home in Chicago to go to Mount Rushmore, $812$ miles away. After $3$ hours, he has gone $190$ miles. At that rate, how long will the whole drive take?

Kelly leaves her home in Seattle to drive to Spokane, a distance of $280$ miles. After $2$ hours, she has gone $152$ miles. At that rate, how long will the whole drive take?

Phil wants to fertilize his lawn. Each bag of fertilizer covers about $\mathrm{4,000}$ square feet of lawn. Phil’s lawn is approximately $\mathrm{13,500}$ square feet. How many bags of fertilizer will he have to buy?

April wants to paint the exterior of her house. One gallon of paint covers about $350$ square feet, and the exterior of the house measures approximately $2000$ square feet. How many gallons of paint will she have to buy?

What number is $\text{35\%}$ of $250?$

What number is $\text{75\%}$ of $920?$

What number is $\text{110\%}$ of $47?$

What number is $\text{150\%}$ of $64?$

$45$ is $\text{30\%}$ of what number?

$25$ is $\text{80\%}$ of what number?

$90$ is $\text{150\%}$ of what number?

$77$ is $\text{110\%}$ of what number?

What percent of $85$ is $17?$

What percent of $92$ is $46?$

What percent of $260$ is $340?$

What percent of $180$ is $220?$

What number is $\text{65\%}$ of $180?$

What number is $\text{55\%}$ of $300?$

$\text{18\%}$ of $92$ is what number?

$\text{22\%}$ of $74$ is what number?

$\text{175\%}$ of $26$ is what number?

$\text{250\%}$ of $61$ is what number?

What is $\text{300\%}$ of $488?$

What is $\text{500\%}$ of $315?$

$\text{17\%}$ of what number is $\text{\$7.65}?$

$\text{19\%}$ of what number is $\text{\$6.46}?$

$\text{\$13.53}$ is $\text{8.25\%}$ of what number?

$\text{\$18.12}$ is $\text{7.55\%}$ of what number?

What percent of $56$ is $14?$

What percent of $80$ is $28?$

What percent of $96$ is $12?$

What percent of $120$ is $27?$

Mixing a concentrate Sam bought a large bottle of concentrated cleaning solution at the warehouse store. He must mix the concentrate with water to make a solution for washing his windows. The directions tell him to mix $3$ ounces of concentrate with $5$ ounces of water. If he puts $12$ ounces of concentrate in a bucket, how many ounces of water should he add? How many ounces of the solution will he have altogether?

Mixing a concentrate Travis is going to wash his car. The directions on the bottle of car wash concentrate say to mix $2$ ounces of concentrate with $15$ ounces of water. If Travis puts $6$ ounces of concentrate in a bucket, how much water must he mix with the concentrate?

To solve “what number is $\text{45\%}$ of $350\text{”}$ do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

To solve “what percent of $125$ is $25\text{”}$ do you prefer to use an equation like you did in the section on Decimal Operations or a proportion like you did in this section? Explain your reason.

$\text{32\%}$ admission rate for the university

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

$13$ out of $100$ architects are women.

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

$$\text{48\%}$$

$$\text{175\%}$$

$$\text{64.1\%}$$

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

$$\text{6\%}$$

$$\text{23\%}$$

$$\text{128\%}$$

4.9%

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 $\text{12.5\%}.$

$$0.04$$

$$0.15$$

$$2.82$$

$$3$$

$$0.003$$

$$1.395$$

$$\frac{3}{4}$$

$$\frac{11}{5}$$

$$3\frac{5}{8}$$

$$\frac{2}{9}$$

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.

What number is $\text{46\%}$ of $350?$

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

$84$ is $\text{35\%}$ of what number?

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

$\text{200\%}$ of what number is $50?$

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

What percent of $120$ is $81.6?$

What percent of $340$ is $595?$

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?

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.

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.

Andy bought a piano for $\text{\$4,600}.$ The sales tax on the purchase was $\text{\$333.50}.$

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

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 $\text{\$895}?$

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?

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 $\text{\$312}.$

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 $\text{\$45}.$

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 $\text{\$79.99}.$

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?

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?

$3$ is to $8$ as $12$ is to $32.$

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

$1$ teacher to $18$ students is the same as $23$ teachers to $414$ students.

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

$$\frac{5}{13}=\frac{30}{78}$$

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

$$\frac{12}{18}=\frac{6.99}{10.99}$$

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

$$\frac{x}{36}=\frac{5}{9}$$

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

$$\frac{1.2}{1.8}=\frac{d}{6}$$

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

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?

What number is $\text{62\%}$ of $395?$

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

What percent of $\mathrm{1,000}$ is $15?$

What percent of $140$ is $210?$

What number is $\text{85\%}$ of $900?$

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

$\text{\$3.51}$ is $\text{4.5\%}$ of what number?

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