Question

Help Mary ann and carlos are each saving for new scooters. Their savings are shown. Let x represent the number of hours each person works y represent the total earnings in dollars

after how many hours of work will mary ann and carlos have saved the same amount?

Answer 1

4 hours

Explanation:

First, create a linear equation for Carlos using the graph.

Two points on the line: (0, 2) and (1, 10)

`\implies \sf slope\:(m)=(change\:in\:y)/(change\:in\:x)=(10-2)/(1-0)=8`

Use the point-slope equation with the found slope and one of the points:

`\implies y-y_1=m(x-x_1)`

`\implies y-2=8(x-0)`

`\implies y=8x+2`

Now equate the equations for Mary Ann and Carlos, and solve for x:

`\implies 6x+10=8x+2`

`\implies 8=2x`

`\implies x=4`

Therefore, Mary Ann and Carlos have saved the same amount after 4 hours work.

Answer 2

• 4 hours

Explanation:

Use a couple of ordered pairs on the graph and get the equation of the line:

• (0, 2), (1, 10)

The y-intercept is 2 and the slope is 10 - 2 = 8

The line is

• y = 8x + 2

Solve the system of equations by substitution to find the intersection

• y = 6x + 10
• y = 8x + 2

• 6x + 10 = 8x + 2
• 8x - 6x = 10 - 2
• 2x = 8
• x = 4

They will work 4 hours to get same amount of saving