A coin bank contains twice as many nickels as quarters, three times as many pennies as quarters, and no dimes. If the bank contains $7.60 how many of each coin does it contain ?
25q + 5(2q) + 1(3q) = 760
38q = 760
q = 20
so, 20 quarters, 40 nickels, 60 pennies
To solve this problem, we need to set up a system of equations based on the given information. Let's define the number of quarters, nickels, and pennies in the coin bank.
Let's say, for simplicity, that the number of quarters is 'Q'.
Based on the given information:
- The number of nickels is twice the number of quarters, so it would be 2Q.
- The number of pennies is three times the number of quarters, so it would be 3Q.
Now, let's assign the values to the coins:
- A quarter is worth $0.25.
- A nickel is worth $0.05.
- A penny is worth $0.01.
We can now set up the equation for the total value in the coin bank:
0.25Q + 0.05(2Q) + 0.01(3Q) = 7.60
Simplifying the equation:
0.25Q + 0.10Q + 0.03Q = 7.60
0.38Q = 7.60
Q = 7.60 / 0.38
Q = 20
So, the number of quarters in the coin bank is 20.
Now, we can substitute this value of Q into the expressions for the number of nickels and pennies to find their values:
Number of nickels = 2Q = 2 * 20 = 40
Number of pennies = 3Q = 3 * 20 = 60
Therefore, the coin bank contains 20 quarters, 40 nickels, and 60 pennies.