A change purse contains an equal number of pennies, nickels, and dimes. The total value of the coins is 112 cents. How many coins of each type does the purse contain?
Let x = number of each coin
x + 5x + 10x = 112
Solve for x.
To solve this problem, we need to set up a system of equations. Let's represent the number of pennies, nickels, and dimes as P, N, and D respectively.
Since the change purse contains an equal number of pennies, nickels, and dimes, we can say that:
P = N = D (equation 1)
We also know that the total value of the coins is 112 cents, which can be expressed as:
1P + 5N + 10D = 112 (equation 2)
Now, we can substitute the value of P from equation 1 into equation 2:
1(N) + 5(N) + 10(N) = 112
11N = 112
N = 112 / 11
N ≈ 10.18
Since the number of coins must be a whole number, we can assume that N = 10.
Now, we can substitute the value of N = 10 into equation 1 to find the value of P and D:
P = 10
D = P = 10
So, the change purse contains 10 pennies, 10 nickels, and 10 dimes.