Math Coin Question (Calculus)?

Question

If I have fifteen coins, all nickels and dimes. The nickels change to quarters and the dimes change to nickels, but the value of the money remains the same, how many nickels and dimes do I have?

Answer 1

Let N be the number of nickels

Let D be the number of dimes

Number of coins:

N + D = 15

Original value (nickels worth 5, dimes worth 10):

5N + 10D

New value (nickels worth 25, dimes worth 5):

25N + 5D

Equate these values:

5N + 10D = 25N + 5D

Subtract 5N

10D = 20N + 5D

Subtract 5D

5D = 20N

Divide by 5:

D = 4N

Substitute into the first equation:

N + D = 15

N + 4N = 15

5N = 15

N = 3

D = 12

Double-check:

Original value --> 5(3) + 10(12) = 15 + 120 = 135 cents

New value --> 25(3) + 5(12) = 75 + 60 = 135 cents

Answer:

3 nickels and 12 dimes