Sure, let's solve this problem step by step:
1. Let q be the number of quarters.
2. Since Noel has 2 times as many nickels as quarters,
- The number of nickels will be 2q.
3. Each quarter is worth 25 cents and each nickel is worth 5 cents.
4. Write the equation for the total value of the coins:
- The value of the quarters in cents is [tex]\( 25q \)[/tex].
- The value of the nickels in cents is [tex]\( 5 \times 2q \)[/tex].
5. Combine the values of the quarters and nickels to set up the following equation:
[tex]\[
25q + 5 \times 2q = 175
\][/tex]
6. Simplify the equation:
[tex]\[
25q + 10q = 175
\][/tex]
[tex]\[
35q = 175
\][/tex]
7. Solve for q (the number of quarters):
[tex]\[
q = \frac{175}{35}
\][/tex]
[tex]\[
q = 5
\][/tex]
8. Calculate the number of nickels:
[tex]\[
n = 2 \times q
\][/tex]
[tex]\[
n = 2 \times 5
\][/tex]
[tex]\[
n = 10
\][/tex]
Conclusion:
- Noel has 5 quarters.
- Noel has 10 nickels.
