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Question 83621: joe has a collection of nickels and dimes worth $7.05. if the number of dimes were doubled and the number of nickels were incresed by 5, the value of the coins would be $11.80 how many dimes does he have ?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write an equation for each statement: n=no. of nickels; d = no. of dimes
:
"joe has a collection of nickels and dimes worth $7.05".
.05n + .10d = 7.05; call it eq1
:
"if the number of dimes were doubled and the number of nickels were increased by 5, the value of the coins would be $11.80"
2(.10d) + .05(n+5) = 11.80
.2d + .05n + .25 = 11.80
.05n + .2d = 11.80 - .25; put it in the same order as eq1
.05n + .2d = 11.55; call it eq2
:
Subtract eq1 from eq2:
.05n + .20d = 11.55
.05n + .10d = 7.05
--------------------subtracting eliminates n
0 n + .10d = 4.50
d = 4.50/.10
d = 45 dimes
:
To check our solution, Find the number of nickels using eq1, substitute 45 for d:
.05n + .10(45) = 7.05
.05n + 4.50 = 7.05
.05n = 7.05 - 4.50
.05n = 2.55
n = 2.55/.05
n = 51 nickels
:
Check solution using eq2
.05(51) + .20(45) =
2.55 + 9.00 = 11.55
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