A jar of coins has only nickels and quarters, which are worth a total of $3.25. There are 5 fewer quarters than nickels. How many quarters and nickels are in the jar?
5n + 25q = 325
q = n-5
now just plug in q and solve for n.
To solve this problem, we can use a system of equations. Let's represent the number of nickels as "n" and the number of quarters as "q".
1. From the problem statement, we know that the value of the nickels is 5 cents and the value of the quarters is 25 cents. Therefore, we can write the first equation for the value of the coins:
5n + 25q = 325 (1)
2. We are also given that there are 5 fewer quarters than nickels, which can be expressed as:
q = n - 5 (2)
Now we have a system of two equations that we can solve simultaneously. Let's substitute equation (2) into equation (1) and solve for n:
5n + 25(n - 5) = 325
Simplifying the equation:
5n + 25n - 125 = 325
Combining like terms:
30n - 125 = 325
Adding 125 to both sides:
30n = 450
Dividing by 30:
n = 15
Now that we have the value of n, we can substitute it back into equation (2) to find the value of q:
q = 15 - 5
q = 10
Therefore, there are 15 nickels and 10 quarters in the jar.