Question

Braxton and Maggie babysit children for extra money over the summer. Braxton's income is determined by f(x) = 9x + 10, where x is the number of hours. Maggie's income is g(x) = 6x + 15. If Braxton and Maggie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Braxton works 5 hours. Create the function h(x), and indicate if Braxton will make more money working alone or by teaming with Maggie.

Answer 1

You didn’t explicitly state it, but in order for the problem to not be trivial I’ll assume that Braxton and Maggie split their earnings evenly between them. The total income of both individuals is 9x+10+6x+15 = 14x+25. Since Braxton gets to keep half of this, his earnings partnering is (14x+25)/2 = 7x + 12.5. After 5 hours as a team, he makes 7(5)+12.5=47.5 dollars. Alone, he makes 9(5)+10=55 dollars. This means he makes more money alone with a 5 hour timeframe.