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.
Let's start by assigning variables to the unknown quantities. Let's say Kevin plays for x hours and Jesse plays for y hours.
From the problem, we know that Jesse plays 2 hours more than half the hours that Kevin plays. This can be expressed as y = (x/2) + 2.
We also know that the total number of hours they play is 11, so x + y = 11.
Now, we have a system of equations:
y = (x/2) + 2
x + y = 11
To solve this system, we can use substitution or elimination method. Let's use substitution method:
From the second equation, we can solve for x:
x = 11 - y
Now we can substitute this expression for x into the first equation:
y = ((11 - y)/2) + 2
2y = 11 - y + 4
2y + y = 15
3y = 15
y = 5
Now we can substitute this value for y back into the second equation and solve for x:
x + 5 = 11
x = 11 - 5
x = 6
So, Kevin plays for 6 hours and Jesse plays for 5 hours.
Answer: D) Jesse plays for 5 hours and Kevin plays for 6 hours.