Question

11. Jimmy bought some used video games and used movies at the Movie Barn. He bought a total of 15 items and spent $106 in all, not including tax. Each used video game cost $10 and each used movie

cost $6. How many of each item did he buy?

Answer 1

Jimmy bought 4 used video games and 11 used movies.

Step-by-step explanation:

Let's define the number of used video games as x and the number of used movies as y.

We know that the total number of items is 15, so we can write the equation: x + y = 15. (Equation 1)

We also know that each used video game costs $10 and each used movie costs $6, so we can express the total cost as: 10x + 6y = 106. (Equation 2)

To find the values of x and y, we can solve the system of equations formed by Equation 1 and Equation 2.

Multiplying Equation 1 by 6, we get: 6x + 6y = 90. Subtracting this equation from Equation 2, we eliminate the y variable and solve for x: 10x + 6y - (6x + 6y) = 106 - 90. Simplifying, we get: 4x = 16. Dividing both sides by 4, we find that x = 4.

Substituting the value of x into Equation 1, we can solve for y: 4 + y = 15. Subtracting 4 from both sides, we find that y = 11.

Therefore, Jimmy bought 4 used video games and 11 used movies.

Answer 2

Used Video game = x = 11

Used movie = y = 4

Step-by-step explanation:

Let

Used Video game = x

Used movie = y

x + y = 15 (1)

10x + 6y = 106 (2)

From 1

x = 15 - y

Substitute x = 15 - y into (2)

10x + 6y = 106

10(15 - y) + 6y = 106

150 - 10y + 6y = 106

-10y + 6y = 106 - 150

- 4y = -44

Divide both sides by -4

y = -44/-4

= 11

y = 11

Substitute y = 11 into (1)

x + y = 15

x + 11 = 15

x = 15 - 11

= 4

x = 4

Used Video game = x = 11

Used movie = y = 4