Bank Heist Word Problem

Question

A professional bank heist gang is made up of one driver, one look out, and one experienced robber. After the robbery, the gang meets to divide up their loot according to their agreement.  The robber takes 3/4 of the loot. The lookout takes 2/3 of what is left. The driver takes the rest.

“Hey” she says, “I only got 50 dollars! How much did we steal anyway?”

a. Answer the driver’s question.  Show the mathematical representation (geometric, algebraic, numeric, etc) of the problem used to solve it. Explain your solution, including the correspondence between the elements of the problem, and the components of your representation. 

b. Construct another representation of the problem and show and explain its correspondence with the representation in part a above. 

Answer 1

The robber takes 3/4 of the loot leaving a quarter.
The lookout takes 2/3 of the remaining quarter which is 2/3*1/4=1/6. The driver is left with 1/3 of the quarter=1/12.
The driver's share is $50, so the loot is 12*$50=$600.
The robber has 3/4 of $600=$450, the lookout has 2/3 of $150=$100.

A pie chart is useful in representing the shares.
The pie chart resembles a clock face where a minute division represents $10.
The robber's share is the large segment from 12 o'clock to 9 o'clock; the lookout's from 9 till 11; and the driver's from 11 to 12.