Ethan has $0.75 worth of pennies and nickels. He has 9 more nickels than pennies. Determine the number of pennies and the number of nickels that Ethan has.(1 point)

Question

Responses

3 pennies and 12 nickels
3 pennies and 12 nickels

10 pennies and 19 nickels
10 pennies and 19 nickels

13 nickels and 10 pennies
13 nickels and 10 pennies

5 pennies and 14 nickels

Answer 1

Let's define the number of pennies as \( p \) and the number of nickels as \( n \).

From the problem, we know two things:

1. The total value of the coins is $0.75, which can also be expressed in cents as 75 cents. Since each penny is worth 1 cent and each nickel is worth 5 cents, we can write the following equation based on the total value of the coins:

\[ p + 5n = 75 \]

2. Ethan has 9 more nickels than pennies. This gives us another equation:

\[ n = p + 9 \]

Now we can substitute the second equation into the first equation. Replacing \( n \) in the first equation with \( p + 9 \):

\[ p + 5(p + 9) = 75 \]

Now, simplify the equation:

\[ p + 5p + 45 = 75 \]

Combine like terms:

\[ 6p + 45 = 75 \]

Subtract 45 from both sides:

\[ 6p = 30 \]

Now divide by 6:

\[ p = 5 \]

Using the value of \( p \) to find \( n \):

\[ n = p + 9 = 5 + 9 = 14 \]

Thus, Ethan has 5 pennies and 14 nickels.

Looking at the provided responses, the correct one is: 5 pennies and 14 nickels.