SOLUTION: 17 coins consisting of nickels dimes and quarters are collected for a newspaper vending machine. the total value of the coins is $2.05 and there are 4 more dimes than quarters. fin

Question 149033: 17 coins consisting of nickels dimes and quarters are collected for a newspaper vending machine. the total value of the coins is $2.05 and there are 4 more dimes than quarters. find the number of each coin type.
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
d=number of dimes
n=number of nickels
q=number of quarters
coefficient=value of the coin

d+n+q=17----------------------because there are 17 coins in all
10d+5n+25q=205----------------because the total value is 205 cents
d=q+4-------------------------because there are four more dimes than quarters

Solve for n in the first equation
n=17-d-q
plug in d
n=17-q-4-q or 13-2q

Plug both d and q in the second equation
10(q+4)+5(13-2q)+25q=205

Disitribute
10q+40+65-10q+25q=205

Combine like terms
25q+105=205

Subtract 105 from both sides
25q=100

Divide by 25
q=4

number of quarters= 4

d=q+4
d=4+4
d=8

number of dimes=8

d+n+q=17
8+n+4=17

Simplify
12+n=17

Subtract 12
n=5

number of nickels=5

So,
number of quarters= 4
number of dimes=8
number of nickels=5
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