Question

Melissa has $2.35 in nickels and dimes. If she has 33 coins in all, how do you find the number of nickels and dimes?

Answer 1

`N = 19, D = 14`

Explanation:

Given: `$2.35` in nickels and dimes, `33` coins in all

There are always 2 equations in these types of problems.

The first equation is the quantity equation and the second is the value equation.

The value of a nickel is 5 cents, the value of a dime is 10 cents and `$2.35 = 235` cents.

Let `N = "number of nickels and "D = "number of dimes"`

quantity equation: `" "N + D = 33`

value equation: `" "235 = 5N + 10D` or `2.35 = .05N + .1D`

I think it's easier to not have decimals, so I will be using the first value equation.

We can rewrite the quantity equation to use substitution: `N = 33 - D`

Substitute this into the value equation:

`5(33-D) + 10D = 235`

`165 - 5D + 10D = 235`

`165 + 5D = 235`

`5D = 235 - 165 = 70`

`D = 70/5 = 14`

`N = 33-14 = 19`