Question

Colby and Danielle clean pools for extra money over the summer. Colby's income is determined by f(x) = 3x + 12, where x is the number of hours. Danielle's income is g(x) = 5x + 10. If Colby and Danielle were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Colby works 4 hours. Create the function h(x) and indicate if Colby will make more money working alone or by teaming with Danielle.

h(x) = 2x + 2, work alone
h(x) = 8x + 22, team with Danielle
h(x) = 2x + 2, team with Danielle
h(x) = 8x + 22, work alone

Answer 1

h(x) = f(x) + g(x)=3x + 12+5x + 10.=8x + 22
h(x) = 8x + 22, team with Danielle
f(4)=22, and h(4)=32+22=54, or 54/2=27
so Colby will make more money working by teaming with Danielle.

Answer 2

h(x) = f(x) + g(x) = 3x + 12 + 5x + 10 = 8x + 22

If Colby works alone for 4 hours, income = 3(4) + 12 = 12 + 12 = 24
If Colby teams with Danielle for 4 hours, income = (8(4) + 22)/2 = (32 + 22)/2 = 54/2 = 27

The answers are: h(x) = 8x + 22, team with Danielle