John's Collection:
10 coins in all
2 fewer quarters than dimes
2 quarters
Q =
D =
N =
Q = 4
D = 6
To find the values of Q, D, and N in John's collection, we need to understand that Q represents the number of quarters, D represents the number of dimes, and N represents the number of nickels.
From the information given in the question, we know the following:
1. John has a total of 10 coins.
2. There are 2 fewer quarters than dimes.
3. John has 2 quarters.
Based on this, we can set up equations to solve for the values.
First, we can assign variables to the unknowns:
Let Q = the number of quarters
Let D = the number of dimes
Let N = the number of nickels
Now let's translate the given information into equations:
1. John has a total of 10 coins:
Q + D + N = 10
2. There are 2 fewer quarters than dimes:
Q = D - 2
3. John has 2 quarters:
Q = 2
Now we have a system of equations:
Equation 1: Q + D + N = 10
Equation 2: Q = D - 2
Equation 3: Q = 2
From Equation 3, we know that Q is equal to 2. We can substitute this value into Equation 2:
2 = D - 2
Now we can solve for D:
D = 2 + 2 = 4
Using the value of D, we can substitute it back into Equation 1 to find N:
2 + 4 + N = 10
6 + N = 10
N = 10 - 6 = 4
So, the number of quarters (Q) is 2, the number of dimes (D) is 4, and the number of nickels (N) is also 4.