1550.18 – Jacob's Bumper

Jacob agrees to work after school for Mr. Daniels, his school’s head custodian, who says he'll pay Jacob $240 and the front bumper of a 1958 Ford Thunderbird for one year of work, including the summer. Jacob quits after seven months. Mr. Daniels does some calculation and pays Jacob $100 plus the bumper. What did Mr. Daniels decide was the value of the bumper?

Solution

Let bb be the value of the bumper. We are given that the value of a whole years work is 240+b240 + b. Therefore,

value of one month’s work =112(240+b)=20+b12.\text{value of one month's work } = \dfrac{1}{12}(240 + b) = 20+\dfrac{b}{12}.

So, the value of seven month's work is

7(20+b12)=140+7b12=100+b,7(20 + \dfrac{b}{12}) = 140 + \dfrac{7b}{12} = 100 + b,

where the last part of this equality is what Mr. Daniels actually paid Jacob. Solving for bb we get,

b=140+7b12−1005b12=40b=$96\begin{aligned}b &= 140 + \dfrac{7b}{12} - 100 \\\dfrac{5b}{12} &= 40 \\b &= \$96\end{aligned}