Bruce has $10 in nickels and quarters. The number of nickels is 24 less than twice the number of quarters. How many of each does he have?
+23246 Let n = number of nickels. The value of these nickels is 0.05n.
Let q = number of quarters. The value of these quarters is 0.25q.
The number of nickels is 24 less than twice the number of quarters. ---> n = 2q - 24
The total value of the nickels and quarters is $10.00. ---> 0.05n + 0.25q = 10.00
Substituting: 0.05(2q - 24) + 0.25q = 10.00
0.10q - 1.20 + 0.25q = 10.00
- 1.20 + 0.35q = 10.00
0.35q = 11.20
q = 32 <--- number of quarters
Since n = 2q - 24 ---> n = 2(32) - 24 = 40 <--- number of nickels
