Solving word problems using systems of equations

[Pages:6]Lesson 24 Application of Systems of Equations

Solving word problems using systems of equations

1. At the concessions stand outside Yankee stadium, John bought 3 pretzels and 5 sodas for $15. While Jamie paid $18 for 6 pretzels and 2 sodas. Find the price of a pretzel and the price of a soda.

Let x = price of a pretzel Let y = the price of a soda

3x + 5y = 15 6x + 2y = 18

$2.50 for a pretzel $1.50 for a soda

Lesson 24 Application of Systems of Equations

2. How much 35% red paint and 60% blue paint is needed to make 5 quarts of 50% purple paint?

Let x = quarts of red paint Let y = quarts of blue paint

x + y = 5 35x + 60y = 50(5)

2 quarts of red paint 3 quarts of blue paint

Lesson 24 Application of Systems of Equations

3. Last year Cathy earned $300 on the $5000 she invested. Some of her investments paid 3% dividends and the rest paid 18%. How much money did she invest at each percent?

Let x = amount invested at 3% Let y = amount invested at 18%

x + y = 5000 3x + 18y = 300(100)

$1000 at 18% $4000 at 3%

Lesson 24 Application of Systems of Equations

4. The perimeter of a rectangle is 50 cm. The length is 9 cm more than the width. Find the length and the width of the rectangle.

Let x = width Let y = length

y = x+9 50= 2x + 2y

Length 17 cm Width 8 cm

5. Linda spent $3.60 for stamps to mail packages. Some were 30cent stamps and the rest were 20 cent stamps. The number of 20cent stamps was 2 less than the number of 30cent stamps. How many stamps of each kind did Linda buy?

Let x = # of 20 cent stamps Let y = # of 30 cent stamps

6 20 cent stamps 8 30 cent stamps

x = y 2 .30y + .20x = 3.60

x = y 2 .30y + .20x = 3.60

Lesson 24 Application of Systems of Equations

Lesson 24 Application of Systems of Equations

Problem Set

1. Find two numbers such that the sum of the first and three times the

second is 5 and the sum of second and two times the first is 8.

Let x = 1st number

x + 3y = 5

y = 2nd number

2x + y = 8

2. A chemist has two solutions: a 50% methane solution and an 80%

methane solution. He wants 100 mL of a 70% methane solution. How many

mL of each solution does he need to mix?

Let x = # mL of 50% solution

x + y = 100

y = # mL of 80% solution

.5x + .8y = .7(100)

3. Pam has two part time jobs. At one job, she works as a cashier and makes

$8 per hour. At the second job, she works as a tutor and makes $12 per hour.

One week she worked 30 hours and made $268. How many hours did she

spend at each job?

Let x = # hours at cashier job y = # hours at tutoring job

x + y = 30 8x + 12y = 268

4. A store sells Brazilian coffee for $10 a pound and Columbian coffee for $14 a pound. If they decide to make a 150-pound blend of the two and sell it for $11 a pound, how much of each type of coffee should be used?

Let x = lbs of Brazilian coffee y = lbs. of Columbian coffee

x + y = 150 10x + 14y = 11(150)

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