Question

Five Seconds of Summer homework help service charges a base charge of $25 and $5 per hour. Fall Out Boy's homework help service charges a base fee of $9 and $3 per hour. Write a system of equations to find when each service will cost the same. If you need 20 hours of service, which one is the cheapest?

Answer 1

To find when each service will cost the same, set up a system of equations using the given information. When you need 20 hours of service, Fall Out Boy's service is the cheapest.

Step-by-step explanation:

To find when each service will cost the same, we need to set up a system of equations using the given information. Let x be the number of hours of service.

For the Five Seconds of Summer service, the cost can be represented by the equation C1 = 25 + 5x.

For Fall Out Boy's service, the cost can be represented by the equation C2 = 9 + 3x.

To find when each service will cost the same, we need to set C1 equal to C2 and solve for x:

25 + 5x = 9 + 3x

Subtracting 3x from both sides gives:

2x = 16

Dividing both sides by 2 gives:

x = 8

So, when x = 8, both services will cost the same.

To determine which service is cheapest when you need 20 hours of service, we can substitute x = 20 into both equations and compare the costs.

For Five Seconds of Summer, C1 = 25 + 5(20) = $125.

For Fall Out Boy, C2 = 9 + 3(20) = $69.

Therefore, the cheapest option when you need 20 hours of service is Fall Out Boy's homework help service, which costs $69.