Answer:
- 36 nickels
- 32 dimes
- 12 quarters
Explanation:
You want to know the number of nickels, dimes, and quarters that comprise $8.00, when the number of nickels is 3 times the number of quarters, and 4 more than the number of dimes.
Setup
Let n, d, q represent the numbers of nickels, dimes, and quarters, respectively. The given relations can be written as equations:
5n +10d +25q = 800 . . . . . value of the coins in cents
n = 3q . . . . . . . . 3 times as many nickels as quarters
n -d = 4 . . . . . . . 4 fewer dimes than nickels
Solution
Writing the numbers of dimes and quarters in terms of the number of nickels, we have ...
q = n/3
d = n -4
Substituting these into the last equation gives ...
5n +10(n -4) +25(n/3) = 800
5n +10n -40 +(8 1/3)n = 800 . . . . expand parentheses
(23 1/3)n = 840 . . . . . . . . . . . . . add 40, collect terms
n = 840/(23 1/3) = 36 . . . . . . . divide by the coefficient of n
q = 36/3 = 12
d = 36 -4 = 32
There are 36 nickels, 32 dimes, and 12 quarters.
__
Additional comment
The solution shown is "ad hoc", meaning it is chosen based on the fact that substitutions are made relatively easy by the given relations.
Writing the equations in the form of an augmented matrix allows use of standard tools and procedures, independent of the given coefficients. The attachment shows a calculator solution of the system of equations.