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?

Question

3518 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-03T22:22:21

$N = 19, D = 14$

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:

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

$165 - 5D + 10D = 235$

$165 + 5D = 235$

$5D = 235 - 165 = 70$

$D = 70/5 = 14$

$N = 33-14 = 19$