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?

Tags:
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}