Question

Victor wants to start a lawn care business. He offers his clients two different service options:

Plan A charges $20 per month plus $5 an hour.
Plan B charges $30 per month plus $3 an hour.
He used the system of equations below to determine how much money he can make on both plans.

y = 5x + 20
y = 3x + 30


If x represents the number of hours he works, and y represents the total money he makes at what point will he make the same amount with both plans? Use the graph below to estimate your answer:

Answer 1

Victor will make the same amount of money, which is $45, with both Plan A and Plan B when he works 5 hours.

Step-by-step explanation:

To determine at what point Victor will make the same amount of money with both plans, we need to find the intersection point of the two equations given.

These equations, y = 5x + 20 and y = 3x + 30, represent the total money made from each plan, where x is the number of hours he works and y is the total money he makes.

To find the intersection point, we set the two equations equal to each other because at the intersection point, y will have the same value for both equations.

So we solve for x:

5x + 20 = 3x + 30

2x = 10

x = 5

Now we substitute x back into one of the original equations to find the corresponding y value, which represents the total money made:

y = 5(5) + 20

y = 45

Therefore, Victor will make the same amount of money, $45, with both plans after working 5 hours.