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?

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!

yes. we do proportions in probabilities.

step-by-step explanation:

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