d=2n: there are twice as many dimes as nickels.
n+d+q=52: a total of 52 coins, using d from above in this gives you:
n+2n+q=52 combine like terms on left side
3n+q=52 subtract 3n from both sides
q=52-3n
Then you are told that the coins have a total value of $6 which is equal to 600 cents. So we can say:
25q+10d+5n=600 divide all terms by 5
5q+2d+n=120, and from earlier we saw q=52-3n and d=2n so you have:
5(52-3n)+2(2n)+n=120 expanding...
260-15n+4n+n=120 combining like terms
260-10n=120 subtract 260 from both sides
-10n=-140 divide both sides by -10
n=14, since q=52-3n and d=2n
q=(52-3(14))=52-42=10
d=2(14)=28
So there are 10 quarters, 28 dimes, and 14 nickels or as your choices put it:
q=10, d=28, n=14 (the correct answer is d.)
