Justin has $3.25 worth of dimes and quarters. He has a total of 16 dimes and quarters altogether. Determine the number of dimes and the number of quarters that Justin has.
Let x be the number of dimes and y be the number of quarters.
We have the following equations:
1. x + y = 16 (total number of dimes and quarters)
2. 0.10x + 0.25y = 3.25 (value of dimes and quarters in dollars)
Rewrite equation 2 in terms of whole numbers:
10x + 25y = 325
Now we can solve the system of equations:
From equation 1:
x = 16 - y
Substitute x in equation 2:
10(16 - y) + 25y = 325
160 - 10y + 25y = 325
15y = 165
y = 11
Substitute y back into x = 16 - y:
x = 16 - 11
x = 5
Therefore, Justin has 5 dimes and 11 quarters.