x + y = 11

Question

y = 0.5x + 2

y = Jesse; x = Kevin

Kevin and Jesse like to play video games. They play a total of 11 hours everyday. Jesse plays 2 hours more than half the hours that Kevin plays. How many hours do each of the boys play video games each day? Use system of equations to solve the problem.
Responses

A Jesse plays for 6 hours and Kevin plays for 5 hours.Jesse plays for 6 hours and Kevin plays for 5 hours.

B Jesse plays for 8 hours and Kevin plays for 4 hours.Jesse plays for 8 hours and Kevin plays for 4 hours.

C Jesse plays for 4 hours and Kevin plays for 8 hours.Jesse plays for 4 hours and Kevin plays for 8 hours.

D Jesse plays for 5 hours and Kevin plays for 6 hours.Jesse plays for 5 hours and Kevin plays for 6 hours.

Answer 1

To solve the problem, we have the following system of equations based on the information given:

1. \( x + y = 11 \) (the total hours they play together)
2. \( y = 0.5x + 2 \) (Jesse plays 2 hours more than half the hours that Kevin plays)

Now let's substitute equation (2) into equation (1):

1. Substitute \( y \) in the first equation: \[ x + (0.5x + 2) = 11 \]

2. Combine like terms: \[ x + 0.5x + 2 = 11 \] \[ 1.5x + 2 = 11 \]

3. Subtract 2 from both sides: \[ 1.5x = 9 \]

4. Divide by 1.5: \[ x = 6 \]

Now that we have \( x \), we can find \( y \) using one of the original equations. We will use equation (1):

\[ y = 11 - x \] \[ y = 11 - 6 \] \[ y = 5 \]

Thus, Kevin plays \( x = 6 \) hours, and Jesse plays \( y = 5 \) hours.

Therefore, the answer is:

D. Jesse plays for 5 hours and Kevin plays for 6 hours.