9514 1404 393
Answer:
20
Step-by-step explanation:
Let n, d, q represent the numbers of nickels, dimes, and quarters, respectively. Then we have ...
n + d + q = 45
5n +10d +25q = 700
n -d = -5
__
Using n=d -5, we can substitute into the first two equations:
(d -5) +d + q = 45
2d +q = 50 . . . . add 5, collect terms [eq4]
__
5(d -5) +10d +25q = 700
15d +25q = 725 . . . . . . . . . . add 25, collect terms [eq5]
Multiplying [eq4] equation by 3 and subtracting that from 2/5 of [eq5], we have ...
(2/5)(15d +25q) -3(2d +q) = (2/5)(725) -3(50)
6d +10q -6d -3q = 290 -150
7q = 140 . . . . . . simplify
q = 20 . . . . . . . . divide by 7
There are 20 quarters.
