Identify the number of solutions without solving.

Question

Identify the number of solutions without solving.

Rachel is comparing the cost of two parking garages. Garage A charges a flat fee of $6 per car plus $0.50 per hour. Garage B charges a flat fee of $2 per car plus $1 per hour.

Answer 1

Hello Erika,

Let's call x the the number of hours

Let's call y the cost of parking:

For garage A, a $6 flat fee means you only pay that fee once. The $0.50 per hour means $0.50 is multiplied by whatever the number of hours is. Therefore the function that describes the parking cost for garage A is:

y_A = 6 + 0.50x

For garage B, a $2 flat fee means you only pay that fee once. The $1 per hour means $1 is multiplied by whatever the number of hours is. Therefore the function that describes the parking cost for garage B is:

y_B = 2 + 1*x = 2 + x

As you can tell from the two linear equations:

1. the slope of the line for garage A is 0.5
2. the slope of the line for garage B is 1

Because the slopes are different, the two lines will intersect exactly ONE time. In other words, the number of solutions is one (1).