A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?

Question

dumbcow · Answer

Q + D + N = 30
there are more dimes than nickels
D=2N
$5.50 = 550 cents
each Q is worth 25 cents, D 10 cents, N 5 cents
-> 25Q+10D+5N = 550
solve using substitution
sub 2N for D in top equation
Q +2N +N = 30
Q+3N = 30
3N = 30-Q
N = 10-(1/3)Q
sub this in for N
->25Q +10(2*(10-(1/3)Q))+5(10-(1/3)Q) = 550
distribute and add like terms
(50/3)Q +250 = 550
Q = (550-250)*(3/50)
Q = 90/5 = 18

anonymous · Answer

THANK YOU

dumbcow · Answer

your welcome, follow those steps for any similar problems