Question

Bob and Susie wash cars for extra money over the summer. Bob's income is determined by f(x) = 6x + 13, where x is the number of hours. Susie's income is g(x) = 4x + 18. If Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Bob works 3 hours. Create the function h(x), and indicate if Bob will make more money working alone or by teaming with Susie.

Answer 1

He would make more money with Susie than by himself because if he only works three hours and Susie make more money than him she would have more but if they work as a team they could split the money and get more together.

Answer 2

The function
`h(x) =10x+31` and Bob will make more money by working alone.

Explanation:

Bob's income is determined by
`f(x) = 6x + 13`

Susie's income is
`g(x) = 4x + 18.`

Bob and Susie were to combine their efforts, their income would be h(x) = f(x) + g(x).

So,
`h(x) =(6x+13)+(4x+18)`

`h(x) =10x+31`

Their combined income is determines by
`h(x) =10x+31`

If Bob works for 3 hours alone

So, Bob's income :
`f(x) = 6x + 13`

`f(x) = 6(3) + 13`

`f(x) =31`

If bob works 3 hours in a team

So, Income :
`h(x) =10(3)+31`

`h(x) =30+31`

`h(x) =61`

Since together their income for 3 hours is $61

So, This amount will be divided in two parts

So, Each will earn amount =
`(61)/(2)=30.5`

So, Bob will earn $30.5 working in a team and $31 working alone

So, Bob will make more money by working alone.

Hence the function
`h(x) =10x+31` and Bob will make more money by working alone.