Question

If Corey has 13 nickels and quarters in his pocket, and they have a combined value of 165 cents, how many of each coin does he have?

Answer 1

To find the number of nickels and quarters Corey has, set up and solve a system of equations based on the total coins and their combined value. Corey has 8 nickels and 5 quarters.

Step-by-step explanation:

The student is asking a question related to algebra and the concept of simultaneous equations. Corey has a total of 13 nickels and quarters which combined are worth 165 cents. To solve this, we set up two equations based on the given information:

• Let n be the number of nickels.
• Let q be the number of quarters.

The first equation comes from the number of coins: n + q = 13.

The second equation comes from the total value of the coins in cents: 5n + 25q = 165.

We can solve this system of equations using substitution or elimination to find the values of n and q. For example, using substitution:

1. Solve the first equation for n: n = 13 - q.
2. Substitute n into the second equation: 5(13 - q) + 25q = 165.
3. Simplify and solve for q: q = 5.
4. Substitute q back into the first equation: n = 13 - 5 = 8.

Corey has 8 nickels and 5 quarters.