# 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? ##### 1 Answer Jul 3, 2018 #### Answer: $N = 19 , D = 14$#### 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 $N = \text{number of nickels and "D = "number of dimes}$quantity equation: $\text{ } N + D = 33$value equation: $\text{ } 235 = 5 N + 10 D$or $2.35 = .05 N + .1 D$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 \left(33 - D\right) + 10 D = 235$$165 - 5 D + 10 D = 235$$165 + 5 D = 235$$5 D = 235 - 165 = 70$$D = \frac{70}{5} = 14$$N = 33 - 14 = 19\$