SOLUTION: I have $1.45 in nickels and dimes, if the nickels had been dimes and the dimes had been nickels, I would have $1.25. How many nickels and dimes do I actually have? Please explain

Question 591742: I have $1.45 in nickels and dimes, if the nickels had been dimes and the dimes had been nickels, I would have $1.25. How many nickels and dimes do I actually have? Please explain step by step thank you.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let n = original number of nickels
Let d = original number of dimes
;
Write an equation for each statement:
:
"I have $1.45 in nickels and dimes,"
.05n + .10d = 1.45
:
"if the nickels had been dimes and the dimes had been nickels, I would have $1.25."
.10n + .05d = 1.25
:
Multiply the 1st equation by 2, subtract the 2nd equation
.10n + .20d = 2.90
.10n + .05d = 1.25
-------------------- subtraction eliminates n, find d
0 + .15d = 1.65
d =
d = 11 dimes originally
:
Use the 1st equation to find n, replace d with 11
.05n + .10(11) = 1.25
.05n + 1.10 = 1.25
.05n = 1.25 - 1.10
.05n = .15
n =
n = 3 nickels originally
:
:
Check these solutions using the statement:
if the nickels had been dimes and the dimes had been nickels, I would have $1.25."
3(.05) + .10(11) =
.15 + 1.10 = 1.25; confirms our solutions of n=3, d=11

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