Question

Jacob puts all of his dimes and nickels in his piggy bank. He saved up to a total of 40 coins. Altogether there is a total of $6.00 in his bank. How many pennies and how many nickels does he have in his piggy bank?

Answer 1

There is no possible combination of pennies and nickels that satisfies the given conditions.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let's assume Jacob has x nickels and y pennies in his piggy bank.

From the given information, we know that:

1. The total number of coins in his bank is 40, so x + y = 40.
2. The total value of the coins in his bank is $6.00, which is equal to 600 pennies. So, the value of x nickels is 5x cents, and the value of y pennies is 1y cents. Therefore, 5x + y = 600.

We now have a system of equations:

x + y = 40

5x + y = 600

To solve this system, we can use the method of substitution or elimination. Let's solve it using the elimination method:

1. Multiply the first equation by 5: 5(x + y) = 5(40) ⇒ 5x + 5y = 200
2. Subtract the second equation from the first equation: (5x + y) - (5x + y) = (600 - 200) ⇒ 0 = 400

The result is a contradiction, indicating that there is no solution to this system of equations. Therefore, there is no possible combination of nickels and pennies that satisfies the given conditions.

In conclusion, Jacob does not have any pennies or nickels in his piggy bank.