Kevin and Randy Muise have a jar containing ​coins, all of which are either quarters or nickels. The total value of the coins in the jar is ​$. How many of each type of coin do they​ have?

Answer 1

q+n=t = total number of coins

q=number of quarters, n=number of nickels

25q+5n= v= total value in cents

multiply 1st equation by 5

5q+5n=5t

subtract last equation from 1st to eliminate one variable

25q-5q+ 5n-5n= v-5t

20q=v-5t

divide both sides by 20

q=(v-5)/20= number of quarters

n=t-v=t-v/20+t/4=number of nickels

for example, v=50 cents, t=6 coins

then

q=(50-5(6))/20=20/20=1 quarter

n=6-1=5 nickels