Question

Susan has 27 coins, dimes, or nickels, totaling $2. How many of each coin does she have?

Answer 1

Susan has 13 dimes and 14 nickels.

Step-by-step explanation:

Let's assume Susan has x number of dimes and y number of nickels. According to the given information, the total number of coins is 27, so we can write this as an equation: x + y = 27.

Each dime is worth 10 cents, so the total value of dimes is 10x cents. Each nickel is worth 5 cents, so the total value of nickels is 5y cents. The total value of all the coins is $2, which can be written as an equation: 10x + 5y = 200.

We have two equations with two variables, so we can solve them simultaneously to find the values of x and y. By substituting x = 27 - y in the second equation, we get: 10(27 - y) + 5y = 200. Simplifying this equation, we can find y. Once we find y, we can substitute it back in the first equation to find x.

Let's solve the equations step by step:

1. x + y = 27
2. 10x + 5y = 200
3. 10(27 - y) + 5y = 200
4. 270 - 10y + 5y = 200
5. 270 - 5y = 200
6. -5y = -70
7. y = 14
8. Substituting y = 14 in the first equation, we get x + 14 = 27, so x = 13

Therefore, Susan has 13 dimes and 14 nickels.