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.

h(x) = 2x + 5, work alone

h(x) = 2x + 5, team with Susie

h(x) = 10x + 31, team with Susie

h(x) = 10x + 31, work alone

Answer 1

For this case we have the following functions:

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When Bob and Susie work together we have the following function:

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Substituting values we have:

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Rewriting the function we have:

`image`

For 3 hours of work we have:

If Bob works alone:

`image`

If Bob works as a team:

`image`

Therefore, more money is made if you work as a team.

Answer:

`h (x) = 10x + 31`, team with Susie

Answer 2

we are given with two functions: f(x) = 6x + 13 and g(x) = 4x + 18. We are given with h(x) which is associated with f(x) + g(x). The sum of  6x + 13 + 4x + 18 equal to 10x + 31 indicating  Bob will make more money working alone or by teaming with Susie.  The answer hence to this problem is C. h(x) = 10x + 31, team with Susie