Question

Ice Dream charges $4 to rent ice skates, plus $1.50 per hour to skate. Skating Paradise charges $1 to rent ice skates, plus $3 per hour to skate. Write a system of equations to represent the situation, using h for number of hours and c for cost. For how many hours is the cost for both locations equivalent? what is the cost?

Answer 1

Hey there!

These are slope intercept equations, because they have an initial cost and then a cost based on an independent variable, in this case, time spent skating.

Given the information, Ice Dreams equation would be c=1.5h+4 and Skating Paradise would be c=3h+1

Now, we just put them together to make the systems of equations.

c=1.5h+4

c=3h+1

Now, we need to find a point where the two will meet, which will give us our answer. We just need to solve the system.

Let's solve using elimination.We can multiply the top equation by -2 so we can use elimination.

-2c=-3h-8

c=3h+1

We combine the equations..

-c==7

c=7

Now we can plug this into one of the other equations.

7=3h+1

h=2

Now, we have our solution..

(h,c)=(2,7)

Therefore, after two hours, the cost will be the same, and the cost will be seven dollars.

I hope this helps!