ANSWER
480 pounds of silver and 320 pounds of silver alloy
EXPLANATION
The alloy contains 30% silver and 55% silver alloy.
Let the amount of silver be s.
Let the amount of silver alloy be a.
So, we have that the total amount of alloy is 800 pounds.
This must mean that if we add the amount of silver and silver alloy, we will get 800:
s + a = 800 ____(1)
Also, 30% of s and 55% of a make up 40% of 800 pounds of alloy.
This means that:
30% * s + 55% * a = 800 * 40%
=> 0.3s + 0.55a = 800 * 0.4 (convert percentages to decimals)
=> 0.3s + 0.55a = 320 ____(2)
We now have two simultaneous equations:
s + a = 800 ____(1)
0.3s + 0.55a = 320 ____(2)
From (1):
a = 800 - s
Put that in (2):
0.3s + 0.55(800 - s) = 320
0.3s + 440 - 0.55s = 320
Collect like terms:
0.3s - 0.55s = 320 - 440
-0.25s = -120
Divide through by -0.25:
s = -120 / -0.25
s = 480 pounds
Recall:
a = 800 -s
=> a = 800 - 480
a = 320 pounds
Therefore, 480 pounds of silver and 320 pounds of silver alloy must be used.
