SOLUTION: Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $1

Question 143312: Joe has a collection of nickels and dimes that is worth $5.65. If the number of dimes were doubled and the number of nickels were increased by 8, the value of the coins would be $10.45. How many dimes does he have?
The answer I got is $6.19.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

AT LEAST YOU TRIED BUT THE PROBLEM IS ASKING FOR A NUMBER (HOW MANY DIMES?)-NOT AN AMOUNT.

Let x=number of nickels
And let y=number of dimes
Now, we are told the following ($ understood):
0.05x+0.10y=5.65-----------------------------------------eq1
and
0.05(x+8)+0.10*2y=10.45 simplify
0.05x+0.4+0.20y=10.45 subtract 0.4 from each side
0.05x+0.20y=10.05---------------------------------------eq2
subtract eq1 from eq2 and we get:
0.10y=4.40 divide each side by 0.10
y=44--------------------------------------number of dimes
substitute y=44 into eq1
0.05x+0.10*44=5.65
0.05x+4.40=5.65 subtract 4.40 from each side
0.05x=1.25 divide each side by 0.05
x=25---------------------------------------------number of nickels
CK
25*0.05+44*0.10=5.65
1.25+4.40=5.65
5.65=5.65
and
0.10*88+0.05*33=10.45
8.80+1.65=10.45
10.45=10.45
Hope this helps-----ptaylor

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