Each milkshake costs the same price. The total comes to R1 360. Four friends left early and didn’t pay, everyone must each pay R17 extra. Determine the original number of friends in the group.

Question

A group of friends decides to go for gourmet milkshakes after school. Each milkshake costs the same price. The total bill comes to R1 360. Four friends left early and forgot to pay, so the rest of the group must each pay R17 extra. Determine the original number of friends in the group.

Answer 1

If N is the number of friends in the group then they buy N milkshakes costing R1 360 altogether. One milkshake costs 1360/N

When 4 friends left, N-4 had to pay extra R17(N-4) in total. They also had to pay for their own milkshakes at a cost of (N-4)(1360/N). The total amount paid was 1360 so (N-4)(1360/N)+17(N-4)=1360.

(N-4)(1360/N+17)=1360, 

1360+17N-5440/N-68=1360,

17N-5440/N-68=0,

N-320/N-4=0,

N²-4N-320=0=(N-20)(N+16), so N=20.

CHECK

There were 20 in the group, so a milkshake costs 1360/20=R68.

So 16 people paid R68 each, totalling R1 088. They also had to pay R17 extra=R272.

1088+272=R1 360. In other words, it's as if the milkshakes cost 68+17=R85 each. 85×16=1360.