SOLUTION: Joe has dimes and nickels that total $5.65. If Joe doubles his dimes and adds 20 nickels, his total is $10.15. How many dimes does Joe have?

Question 312735: Joe has dimes and nickels that total $5.65. If Joe doubles his dimes and adds 20 nickels, his total is $10.15. How many dimes does Joe have?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Joe has dimes and nickels that total $5.65.
If Joe doubles his dimes and adds 20 nickels, his total is $10.15.
How many dimes does Joe have?
:
Let n = original no. of nickels
Let d = original no. of dime
the equation
.05n + .10d = 5.65
then
(n+20) = no. of nickels later
2d = = no. of dimes later
the equation
.05(n+20) + .10(2d) = 10.15
.05n + 1 + .2d = 10.15
.05n + .20d = 10.15 - 1
.05n + .20d = 9.15
:
Subtract the 1st equation from the above equation
.05n + .20d = 9.15
.05n + .10d = 5.65
------------------------subtraction eliminates n, find d
.10d = 3.50
d =
d = 35 dimes
:
Find the no. of nickels using the 1st equation
.05n + .10(35) = 5.65
.05n + 3.5 = 5.65
.05n = 5.65 - 3.50
.05n = 2.15
n =
n = 43 nickels
:
:
Check solution in the 2nd equation (63 nickels, 70 dimes)
.05(63) + .10(70) =
3.15 + 7.00 = 10.15
:
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