Answer: he used 60 ounces of
the 40% alloy.
Step-by-step explanation:
Let x represent the number of ounces of alloy containing 40%
silver that was used.
Let y represent the number of ounces of alloy containing 60%
silver that was used.
The weight of the alloy made is 80 ounces. It means that
x + y = 80
The amount of silver contained in the first alloy is 40/100 × x = 0.4x
The amount of silver contained in the second alloy is 60/100 × x = 0.6x
The amount of silver contained in the mixture is 45/100 × 80 = 36
Therefore,
0.4x + 0.6y = 36- - - - - - - - - - - - -1
Substituting x = 80 - y into equation 1, it becomes
0.4(80 - y) + 0.6y = 36
32 - 0.4y + 0.6y = 36
- 0.4y + 0.6y = 36 - 32
0.2y = 4
y = 4/0.2
y = 20
x = 80 - 20
x = 60
