Question 1066531: I have 45 coins all in nickles and dimes. They total $3.10. How many of each do I have (nickles and dimes). Found 2 solutions by ikleyn, jim_thompson5910:Answer by ikleyn(52798) (Show Source):
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I have 45 coins all in nickles and dimes. They total $3.10. How many of each do I have (nickles and dimes).
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Let N be the number of nickels.
Then the number of dimes is (45-N).
Nickels contribute 5N cents to the total.
Dimes contribute 10*(45-N) cents to the total.
The "value" equation is
5N + 10*(45-N) = 310 cents.
5N + 450 - 10N = 310,
-5N = 310 - 450 ---> -5N = -140 ---> N= = 28.
Answer. 28 Nickels and 45-28 = 17 dimes.
The value of the nickels is 5n cents while the value of all the dimes is 10d cents. In total, the value is 5n+10d. This must be set equal to 310 ($3.10 = 310 cents)
So we have this equation
5n+10d = 310
Plug in n = 45-d and solve for d
5n+10d = 310
5(n)+10d = 310
5(45-d)+10d = 310
5(45)+5(-d)+10d = 310
225-5d+10d = 310
225+5d = 310
225+5d-225 = 310-225
5d = 85
5d/5 = 85/5
d = 17
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