Question

Sophie and Marcos are each saving for new bicycles. So far, Sophie has $7 saved and can earn $4 per hour walking dogs. Marcos has $3 saved and can earn $6 per hour at his family's plant nursery. After how many hours of work will Sophie and Marcos have saved the same amount? What will that amount be? Use the system of equations below to complete the graph.

Answer 1

2 hours

Explanation:

You can express each person's total earning as the formula for a line. (y=mx+b) Use the amount per hour that can be earned as the slope (m) and the amount already earned as the y intercept (b)

Sophie: y=4x+7

Marcos: y=6x+3

Since y is the total amount of money saved and you know that both people need to earn the same amount of money, we know that y is the same in both equations so we can use substitution to substitute one of the equations in for y in the other equation like this:

4x+7=6x+3

From here, solve algebraically

Subtract 3

4x+4=6x

Subtract 5x

4=2x

Divide by 2

x=2

So they will have the same amount of money after 2 hours.