# Thread: Find Coins of Each Type

1. ## Find Coins of Each Type

A collection of 50 coins is worth $5.20. There are twelve more nickes than dimes, and the rest of the coins are quarters. How many coins of each type are in the collection? This type of question always gives me a hard time. How do I set up the equation for coin problems? 2. Hello, RTC1996! A collection of 50 coins is worth$5.20.
There are twelve more nickels than dimes, and the rest of the coins are quarters.
How many coins of each type are in the collection?

Let: .$\displaystyle \begin{Bmatrix}N &=& \text{no. of nickels} \\ D &=& \text{no. of dimes} \\ Q &=& \text{no. quarters} \end{Bmatrix}$

There are 50 coins: .$\displaystyle N + D + Q \:=\:50$

Their value is $\displaystyle 520\rlap{/}c\!:\;\;5N + 10D + 25Q \:=\:520$

12 more nickels than dimes: .$\displaystyle N \:=\: D + 12$

Solve the system: . $\displaystyle \begin{bmatrix}N &+& D &+& Q &&=&& 50 \\ 5N &+& 10D &+& 25Q &&=&& 520 \\ N &-& D &&&& = && 12 \end{bmatrix}$

Answer: N = 26, D = 14, Q = 10