Question

Frank and Gertrude mow lawns for extra money over the summer. Frank's income is determined by f(x) = 5x + 15, where x is the number of hours. Gertrude's income is g(x) = 4x + 20. If Frank and Gertrude were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Frank works 4 hours. Create the function h(x), and indicate if Frank will make more money working alone or by teaming with Gertrude

Answer 1

a) h(x) = f(x) +g(x)
.. h(x) = (5x +15) +(4x +20)
.. h(x) = 9x +35

b) f(4) = 5*4 +15 = 35
.. h(4) = 9*4 +35 = 71
If Frank gets half their combined pay for working the same time period, he makes more money by splitting with Gertrude (who loses money in the deal).

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Frank breaks even in the team by working 5 hours. When he works more time than that, he's better off by himself. (The reverse is true for Gertrude.)