Question

Logan is buying equipment for the football team and the baseball team. He spends $40 on football uniforms, and he plans on purchasing some footballs. Logan uses this equation to show the total cost of football equipment, y, based on the number of footballs purchased, x. y = 40 + 10x Logan also spends $200 on baseball uniforms, and he plans on purchasing some baseballs. Logan uses this equation to show the total cost of baseball equipment, y, based on the number of baseballs purchased, x. y = 200 + 2x Logan wants to spend the same amount of money on the football team and the baseball team, and he wants to purchase the same number of footballs and baseballs. The coordinate pair that represents this solution is ( , ).

Answer 1

The coordinate pair that represents this solution is (20 , 240)

Step-by-step explanation:

We are given that:

1- Equation that represents amount paid on football team based on number of purchased footballs is:

y = 40 + 10x

2- Equation that represents amount paid on baseball team based on number of purchased baseballs is:

y = 200 + 2x

Now, Logan wants to spend the same amount of money on both teams. This means that the y value in both equations should be equal

He also wants to buy the same number of balls for the two teams. This means that the x value in both equations should also be equal.

Therefore, we would be getting the point of intersection between the two equations.

To do this, we will start by equating the two equations and solving for x as follows:

40 + 10x = 200 + 2x

10x - 2x = 200 - 40

8x = 160

x = 20

Then, we will use the x to substitute in any of the two equations:

Substituting in the first equation:

y = 40 + 10x = 40 + 10(20) = 240

Substituting in the second equation (as a check):

y = 200 + 2x = 200 + 2(20) = 240

Based on the above calculations:

If Logan bought 20 balls for each team, he will be spending $240 on each

Solution set is (20, 240)

Note: the graphical solution is attached.

Hope this helps :)