Question

systems of equations word problems
for each system of equations, define your variables, write a system of equations, and
solve. make sure to interpret your results (ex: there were 7 student tickets sold and 12
adult tickets sold, etc.). you may solve using graphing, substitution, or elimination.
show appropriate work. you may attach graph paper for your graphs if necessary.

1. a used book store also started selling used cds and videos. in the first week, the store

sold a combination of 40 cds and videos. they charged $4 per cd and $6 per video and
the total sales were $180. determine the total number of cds and videos sold.

variable x
variable y

equation 1
equation 2

1. dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins

in all. upon completing the job he counted out the coins and it came to $6.60. how
many of each coin did he earn?

variable x
variable y

equation 1
equation 2

Explanation:

Problem 1

Step1: Define variables

Let \( x \) be the number of CDs sold, and \( y \) be the number of videos sold.

Step2: Write equations

From the total number of CDs and videos: \( x + y = 40 \)
From the total sales: \( 4x + 6y = 180 \)

Step3: Solve the system (using elimination)

Multiply the first equation by 4: \( 4x + 4y = 160 \)
Subtract this from the second equation: \( (4x + 6y) - (4x + 4y) = 180 - 160 \)
Simplify: \( 2y = 20 \), so \( y = 10 \)
Substitute \( y = 10 \) into \( x + y = 40 \): \( x + 10 = 40 \), so \( x = 30 \)

Step1: Define variables

Let \( x \) be the number of dimes, and \( y \) be the number of nickels.

Step2: Write equations

From the total number of coins: \( x + y = 80 \)
From the total value (in cents, so \( \$6.60 = 660 \) cents): \( 10x + 5y = 660 \)

Step3: Solve the system (using elimination)

Multiply the first equation by 5: \( 5x + 5y = 400 \)
Subtract this from the second equation: \( (10x + 5y) - (5x + 5y) = 660 - 400 \)
Simplify: \( 5x = 260 \), so \( x = 52 \)
Substitute \( x = 52 \) into \( x + y = 80 \): \( 52 + y = 80 \), so \( y = 28 \)

Answer:

Variable \( x \): number of CDs sold
Variable \( y \): number of videos sold
Equation 1: \( x + y = 40 \)
Equation 2: \( 4x + 6y = 180 \)
Number of CDs sold: 30, Number of videos sold: 10

Problem 2