Monica was collecting quarters and nickels in a jar. She kept track of the total value of the coins, as well as, how many coins were actually in the jar. However, she forgot specifically to track how many of each coin there is in the jar. If the total value of all the coins is $5.60 and there are 46 coins, how many nickels and quarters are in the jar?
To solve this problem, we can set up a system of equations using the given information. Let's denote the number of quarters as "q" and the number of nickels as "n".
We know that the total value of the coins is $5.60. Quarters have a value of 25 cents each and nickels have a value of 5 cents each. We can express this information in the following equation:
0.25q + 0.05n = 5.60 --- Equation 1
We also know that the total number of coins is 46. So, we can write another equation:
q + n = 46 --- Equation 2
Now, let's solve this system of equations to find the values of q and n.
We can start by multiplying Equation 2 by 0.05 to match the coefficient of "n" in Equation 1:
0.05q + 0.05n = 2.30 --- Equation 3
By subtracting Equation 3 from Equation 1, we can eliminate the variable "n":
0.25q + 0.05n - (0.05q + 0.05n) = 5.60 - 2.30
This simplifies to:
0.20q = 3.30
Dividing both sides of the equation by 0.20, we get:
q = 16.5
Since the number of coins cannot be a fraction, this implies that Monica has 16 quarters (q) in the jar.
Now, we can substitute the value of q into Equation 2 to find the value of n:
16 + n = 46
Subtracting 16 from both sides, we get:
n = 46 - 16
n = 30
Therefore, Monica has 16 quarters and 30 nickels in the jar.