Question

1. Brix has PHP 4000 in denominations of P500 and P100. He has a total of 20 bills. How many of each bill does he have?
2. Several persons rented a boat for P3000 sharing the cost equally. If there had been one more person in the group, each person paid P100 less. How many people were in the group originally?

Answer 1

1) Let there be x bills of P500.

Then, there are (20-x) bills of P100.

By given condition we have,

500*x+100*(20-x) = 4000

i.e., 500x+2000-100x = 4000

i.e., 400x+2000 = 4000

i.e., 400x = 2000

i.e., x = 2000/400

i.e., x = 5

Therefore, there are 5 bills of P500 and (20-5) = 15 bills of P100.

2) Let there be x persons.

Then by the given conditions we have,

(3000/x)-(3000/(x+1)) = 100

i.e., 3000×[(1/x)-(1/(x+1))] = 100

i.e., 3000×[(x+1)-x]/[x(x+1)] = 100

i.e., 3000/[x(x+1)] = 100

i.e., 3000/100 = x(x+1)

i.e., x(x+1) = 30

i.e., x²+x-30 = 0

i.e., (x-5)(x+6) = 0

i.e., x = 5, -6

Since the number of person cannot be negative, then x -6.

Therefore, the required number of people in the group was 5.