Final answer:
The student has 13 nickels and 6 quarters, which adds up to a total of 19 coins and a value of $2.15. This is found by setting up and solving a system of linear equations.
Step-by-step explanation:
To find out how many nickels and quarters the student has, we can set up a system of equations based on the value of the coins and their quantity.
Let's let N represent the number of nickels and Q represent the number of quarters. The value of a nickel is $0.05 and the value of a quarter is $0.25. We are given that the total number of coins is 19 and their combined value is $2.15.
We have two equations:
- The first equation represents the total number of coins: N + Q = 19
- The second equation represents the total value of the coins: 0.05N + 0.25Q = 2.15
To solve the system of equations, we can use substitution or elimination. Let's use substitution in this case. From the first equation, we get N = 19 - Q. Substitute N into the second equation:
0.05(19 - Q) + 0.25Q = 2.15
This simplifies to:
0.95 - 0.05Q + 0.25Q = 2.15
Combining like terms, we get:
0.20Q = 1.20
Divide both sides by 0.20 to find Q:
Q = 6
If Q is 6, then we substitute back into N = 19 - Q to find N:
N = 19 - 6
N = 13
Therefore, the student has 13 nickels and 6 quarters.