Question

Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. The system of linear equations below represents y, the total amount earned in dollars for x days of dog sitting.
1. Write the equation to represent Layla’s fees
2. Write the equation to represent Sam’s fees
3. After how many days do Layla and Sam earn the same amount for dog sitting?
What is that amount?

Answer 1

1. The equation that represents Layla's fees according to the information provided is: y= 2x+3, where:

y is the amount earned

x is the number of days

2. The equation that represents Sam's fees according to the information provided is: y= 3x, where:

y is the amount earned

x is the number of days

3. In the graph, you can see that there is a point in which the two lines intercept. In that point, both earn the same amount that is 9 and the number of days is 3. Also, you can find the answer doing the following:

2x+3= 3x

3= 3x-2x

x= 3

Layla and Sam will earn the same amount for dog sitting after 3 days.

-That amount is: $9.

2x+3= 2(3)+3=  9

3x= 3(3)= 9