Question

Brianna has nickels, dimes, and quarters worth 2.95 in her purse. The number of dimes is eleven less than the sum of the number of nickels and quarters. How many of each type of goin does she have if there are 19 coins in all?

Answer 1

Given

Brianna has nickels(N), dimes (D), and quarters(Q) worth 2.95

Recall

1 dime = $0.1

1 Nickel =$0.05

1 quarter =$0.25

Therefore;

0.1D + 0.05N + 0.25Q =2.95.....equation(i)

The number of dimes is eleven less than the sum of the number of nickels and quarters means D = N + Q -11.... equation(ii)

Having 19 in all means D + N + Q= 19... equation(iii)

Let's rearrange the equations

0.05N+ 0.1D + 0.25Q =2.95.....Equation (i)

N-D+Q=11 ...Equation (ii)

N+D+Q=19 ...Equation (iii)

Solving the three systems equation using Cramer's rule, we have;

N=6, D= 4 and Q=9