Final answer:
After 8 hours, both homework help services charge the same amount. For anyone needing 15 hours of help per month, Fall Out Boy's service, with its lower hourly rate and base fee, is more cost-effective.
Step-by-step explanation:
The question involves finding out after how many hours two different homework help services will charge the same amount. One service has a base charge of $25 and charges an additional $5 per hour, whereas Fall Out Boy's service has a base fee of $9 and charges $3 per hour. To compare the two, we set up equations for each service and find the point at which they equal each other.
Let's define 'x' as the number of hours of service. For the first service, the cost can be represented as C = 25 + 5x. For Fall Out Boy's service, the cost can be represented as C = 9 + 3x. So, to find the number of hours after which both services charge the same, we set these two equations equal: 25 + 5x = 9 + 3x.
Solving for 'x' gives us 2x = 16, so x = 8. This means that after 8 hours, both services will charge the same amount. Now, to figure out which service is better for someone needing 15 hours of help per month, we can calculate the total cost for each service. The first service would cost 25 + (5*15) = $100, and Fall Out Boy's service would cost 9 + (3*15) = $54. Clearly, Fall Out Boy's service is more affordable for 15 hours of help per month.