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Ben needs to convert $1000 to the Japanese Yen. One American dollar is worth 123.3 Yen. How much Yen will he have?

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A golden retriever weighing 85 pounds has diarrhea. His medicine is prescribed as 1 teaspoon per 5 pounds. How much medicine should he be given?

17 tsp

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Five-year-old Lacy was stung by a bee. The dosage for the anti-itch liquid is 150 mg for her weight of 40 pounds. What is the dosage per pound?

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Karen eats 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?

3 4 cup

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An oatmeal cookie recipe calls for 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?

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Solve Similar Figure Applications

In the following exercises, Δ A B C is similar to Δ X Y Z . Find the length of the indicated side.

The above image shows two triangles. The larger triangle is labeled A B C. The length from A to B is 15. The length from A to C is b. The length from B to C is 9. The smaller triangle is labeled X Y Z. The length from X to Y is 10. The length from X to Z is 8. The length from Y to Z is x.

In the following exercises, Δ D E F is similar to Δ N P Q .

The above image shows two triangles side by side. The smaller triangle is labeled D E F. The length from E to D is five-halves. The length from D to F is 7. The length from E to F is d. The second triangle is labeled N P Q. the length from P to N is zero. The length from N to Q is 9. The length from Q to P is eleven-halves.

Find the length of side d .

77 18

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Find the length of side q .

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In the following two exercises, use the map shown. On the map, New York City, Chicago, and Memphis form a triangle whose sides are shown in the figure below. The actual distance from New York to Chicago is 800 miles.

The above image shows a triangle. Each angle is labeled, clockwise, “Chicago”, “New York”, and “Memphis”. The side that extends from Chicago to New York is labeled 8 inches. The side that extends from New York to Memphis is labeled 9.5 inches and the side extending from Memphis to Chicago is labeled 5.4 inches.

Find the actual distance from New York to Memphis.

950 miles

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Find the actual distance from Chicago to Memphis.

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In the following two exercises, use the map shown. On the map, Atlanta, Miami, and New Orleans form a triangle whose sides are shown in the figure below. The actual distance from Atlanta to New Orleans is 420 miles.

The above image shows a triangle. Each angle is labeled, clockwise, “Atlanta”, “Miami”, and “New Orleans”. The side that extends from Atlanta to Miami is labeled 3 inches. The side that extends from Miami to New Orleans is labeled 3.4 inches and the side extending from New Orleans to Atlanta is labeled 2.1 inches.

Find the actual distance from New Orleans to Miami.

680 miles

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Find the actual distance from Atlanta to Miami.

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A 2 foot tall dog casts a 3 foot shadow at the same time a cat casts a one foot shadow. How tall is the cat?

2 3 foot ( 8 in )

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Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?

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The tower portion of a windmill is 212 feet tall. A six foot tall person standing next to the tower casts a seven foot shadow. How long is the windmill’s shadow?

247.3 feet

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The height of the Statue of Liberty is 305 feet. Nicole, who is standing next to the statue, casts a 6 foot shadow and she is 5 feet tall. How long should the shadow of the statue be?

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Everyday math

Heart Rate At the gym, Carol takes her pulse for 10 seconds and counts 19 beats.

  1. How many beats per minute is this?
  2. Has Carol met her target heart rate of 140 beats per minute?

114 beats per minute
no

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Heart Rate Kevin wants to keep his heart rate at 160 beats per minute while training. During his workout he counts 27 beats in 10 seconds.

  1. How many beats per minute is this?
  2. Has Kevin met his target heart rate?
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Cost of a Road Trip Jesse’s car gets 30 miles per gallon of gas.

  1. If Las Vegas is 285 miles away, how many gallons of gas are needed to get there and then home?
  2. If gas is $3.09 per gallon, what is the total cost of the gas for the trip?

19 gallons
$58.71

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Cost of a Road 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.

  1. How many gallons of gas will Danny need to get to and from Phoenix?
  2. If gas is $3.19 per gallon, what is the total cost for the gas to drive to see his grandfather?
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Lawn Fertilizer Phil wants to fertilize his lawn. Each bag of fertilizer covers about 4,000 square feet of lawn. Phil’s lawn is approximately 13,500 square feet. How many bags of fertilizer will he have to buy?

4 bags

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House Paint 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?

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Cooking Natalia’s pasta recipe calls for 2 pounds of pasta for 1 quart of sauce. How many pounds of pasta should Natalia cook if she has 2.5 quarts of sauce?

5

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Heating Oil A 275 gallon oil tank costs $400 to fill. How much would it cost to fill a 180 gallon oil tank?

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Writing exercises

Marisol solves the proportion 144 a = 9 4 by ‘cross multiplying’, so her first step looks like 4 · 144 = 9 · a . Explain how this differs from the method of solution shown in [link] .

Answers will vary.

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Find a printed map and then write and solve an application problem similar to [link] .

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has three rows and four columns. The first row is a header row and it labels each column. The first column is labeled

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Practice Key Terms 2

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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