Question

Ethan has $0.75 worth of pennies and nickels.He has 9 more nickels than penneis. Determine the number of pennies and the number of nickels that Ethan has.

Answer 1

Let \( p \) represent the number of pennies that Ethan has, and let \( n \) represent the number of nickels. According to the problem, we have the following information:

1. The total value of the pennies and nickels is $0.75. Since each penny is worth $0.01 and each nickel is worth $0.05, we can express this as:
\[
0.01p + 0.05n = 0.75
\]

2. Ethan has 9 more nickels than pennies, which can be written as:
\[
n = p + 9
\]

Now, we can substitute the second equation into the first equation. First, let's express the first equation in terms of \( p \) only:

By substituting \( n \):
\[
0.01p + 0.05(p + 9) = 0.75
\]

Now, distribute \( 0.05 \) in the equation:
\[
0.01p + 0.05p + 0.45 = 0.75
\]

Combine the \( p \) terms:
\[
0.06p + 0.45 = 0.75
\]

Next, we can isolate \( p \) by subtracting \( 0.45 \) from both sides:
\[
0.06p = 0.75 - 0.45
\]
\[
0.06p = 0.30
\]

Now, divide both sides by \( 0.06 \) to find \( p \):
\[
p = \frac{0.30}{0.06} = 5
\]

Now that we have the number of pennies, we can use the second equation to find \( n \):
\[
n = p + 9 = 5 + 9 = 14
\]

So, the solution is:
- Number of pennies = \( 5 \)
- Number of nickels = \( 14 \)

To confirm, let's check the total value:
- Value from pennies: \( 5 \times 0.01 = 0.05 \)
- Value from nickels: \( 14 \times 0.05 = 0.70 \)
- Total value: \( 0.05 + 0.70 = 0.75 \)

The calculations are correct. Therefore, Ethan has:

\[
\text{Number of Pennies} = 5, \quad \text{Number of Nickels} = 14
\]