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). Create the new function h(x). If Colby works 4 hours and Danielle works 4 hours, and if they each get half of the money when they work together, will Colby make more money working alone or by teaming with Danielle?

Answer 1

B

Explanation:

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

Answer 2

Colby makes more money by teaming with Danielle

Explanation:

Colby's income =f(x) = 3x+12

and Danielle's income = g(x) = 5x+10

If they combine their efforts the combined income would be

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

If shared equally between them

Colby would get 1/2(8x+22) = 4x+11 and

Danielle would get 1/2(8x+22) = 4x+11

Since given they worked each for 4 hours

Colby income = Danielle income= 4(4) +11 = 27

If not combined, then

Colby income 3(4) + 12=24 and

Danielle income= 5(4) +10 = 30

Because of combining Colby makes more money by teaming with Danielle.

The difference is 3 for 4 hours work.