Problem Solving

Princeton Review

At a restaurant, all tips are added together to be split among the employees at the end of a shift. The four waiters combined get 2/3 of the money, the manager received 1/4 and the busboy receives the remainder. If 1 waiter and the busboy together received $30, how much money was earned in tips for the entire shift?

A. $90
B. $96
C. $108
D. $120
E. $180

OA D

The total tips = x
$$Manager\ receives=\frac{1}{4}x$$
$$4\ waiters\ receivs=\frac{2}{3}x$$
$$1\ waiter\ receives=\left(\frac{2}{3}\cdot\frac{1}{4}\right)x=\frac{1}{6}x$$
$$Busy\ boy\ receives=Total\ tips-\left(tips\ for\ 4waiters\right)-tips\ for\ Manager$$ $$=x-\frac{2}{3}x-\frac{1}{4}x$$ $$=\left(1-\frac{2}{3}-\frac{1}{4}\right)x$$ $$=\left(\frac{12-8-3}{12}\right)x=\frac{1}{12}x$$

Waiters tip + Busyboy's tip = 30 dollars

$$=\frac{1}{6}x+\frac{1}{12}x=30$$ $$\left(\frac{2+1}{12}\right)x=30$$ $$\left(\frac{3}{12}\right)x=30$$ $$\left(\frac{1}{4}\right)x=30$$ $$x=120 dollars$$

Total tips = 120 dolllars
$$Answe\ is\ Option\ D$$