Question

The value of a number of nickels and quarters is $3.25. If the number of nickels was increased by 3 and the number of quarters was doubled, the value would be $5.90. How do you find the number of each?

Answer 1

There are 10 quarters and 15 nickles needed to make $3.25 and $5.90 given the changes identified in the problem.

Explanation:

Let us have the number of quarters equal "q" and the number of nickles equal "n".

"The value of a number of nickels and quarters is $3.25" can then be written as:

`0.05n + 0.25q = 3.25` This is because each nickle is worth 5 cents and each quarter is worth 25 cents.

If the number of nickels was increased by 3 can be written as `n + 3` and "the number of quarters was doubled" can be written as `2q` then the second equation can be written as:

`(n + 3)0.05 + 0.25(2q) = 5.90` or `0.05n + 0.5q = 5.75`

Solving the first equation for `n` gives:

`0.05n + 0.25q - 0.25q = 3.25 - 0.25q`

`0.05n = 3.25 - 0.25q`

`(0.05n)/0.05 = 3.25/0.05 - (0.25q)/0.05`

`n = 65 - 5q`

Substituting `65 - 5q` for `n` in the second equation allows us to determine `q` or the number of quarters.

`0.05(65 - 5q) + 0.5q = 5.75`

`3.25 - 0.25q + 0.5q = 5.75`

`3.25 + 0.25q - 3.25 = 5.75 - 3.25`

`(0.25q)/0.25 = 2.5/0.25`

`q = 10`

Substituting `10` for `q` in the first equation (`n = 65 - 5q`) allows us to determine `n` or the number of nicklesL

`n = 65 - 5*10`

`n = 65 - 50`

`n = 15`