Question

tammy has 35 coins - all nickels and quarters. If she has a total of $5.35, how many of each coin does she have

Answer 1

To solve the problem, we set up two equations representing the total number of coins (35) and their total value ($5.35). By solving the system of equations, we find that Tammy has 17 nickels and 18 quarters.

Step-by-step explanation:

Tammy has 35 coins consisting of nickels and quarters, and the total value of these coins is $5.35. To solve for the number of each type of coin, we can set up a system of equations. Let the number of nickels be represented by n and the number of quarters be represented by q.

We have two equations based on the information given:

1. The total number of coins is 35, so n + q = 35.
2. The total value of the coins is $5.35. Since nickels are worth $0.05 and quarters are worth $0.25, we can write the equation as 0.05n + 0.25q = 5.35.

To solve the system, multiply the first equation by -0.05 to eliminate n when we add the equations:

• -0.05n - 0.05q = -1.75
• 0.05n + 0.25q = 5.35

Adding these equations, we get:

• 0.20q = 3.60

Solving for q, we find that:

• q = 18

Then, substituting q = 18 into the first equation, we find:

• n + 18 = 35
• n = 17

Tammy has 17 nickels and 18 quarters.