In Jamison's backpack, he only keeps nickels and quarters. He has 30 coins in all. How many of each coin does he have? Show work.
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Ok well that was how it was written on my homework so I guess there was an error on the paper. Thanks! That's what I thought.
To solve this problem, let's assign variables to represent the number of nickels and quarters in Jamison's backpack.
Let's say:
N = number of nickels
Q = number of quarters
From the problem, we know that Jamison has a total of 30 coins, so we can create an equation based on the given information:
N + Q = 30 (Equation 1)
We also know that nickels are worth 5 cents each and quarters are worth 25 cents each. If we convert the number of nickels to cents (5N) and the number of quarters to cents (25Q) and add them together, it should equal the total value in cents:
5N + 25Q = total value in cents
Since the total value in cents is not specified in the problem, we cannot further proceed with this approach.
However, we can try a different approach using the given information. We know that Jamison has a total of 30 coins. Let's assume he has all nickels, so the number of nickels would be 30. In that case, the total value in cents would be 5 * 30 = 150 cents.
Since the total value cannot be equal to 150 cents (as per the given information), we can deduce that Jamison must have some quarters as well. Let's try subtracting a quarter and adding a nickel to the previous assumption:
N - 1 + Q + 1 = 30.
This equation can be simplified to: N + Q = 30 (Equation 1) which is the same as the initial equation.
Therefore, we can conclude that there is no unique solution to this problem. Jamison could have various combinations of nickels and quarters that would add up to 30 coins.
For example, he could have 10 nickels (N = 10) and 20 quarters (Q = 20), or 15 nickels (N = 15) and 15 quarters (Q = 15), among other possibilities.