Answer:
69.5 tons of Alloy 1 (of 45% silver) and 69.5 tons of Alloy 2 (of 95% silver) is needed to make 139 tons of 75% silver alloy
Step-by-step explanation:
Given
[tex]Alloy\ 1 = 45\%[/tex]
[tex]Alloy\ 2 = 95\%[/tex]
Required
How much of each alloy is needed for 70% silver alloy 139 tons
Let the amount of alloy 1 needed be x and the amount of 2 needed by y.
So:
[tex]x + y = 139[/tex]
Make y the subject
[tex]y = 139 - x[/tex]
The percentage of each needed is represented as:
[tex]45\% * x + 95\% * y = 139[/tex]
[tex]45\% * x + 95\% * y = 70\% * 139[/tex]
[tex]0.45x + 0.95y = 0.70 * 139[/tex]
[tex]0.45x + 0.95y = 97.3[/tex]
Substitute 139 - x for y in the above equations
[tex]0.45x + 0.95*(139-x) = 97.3[/tex]
[tex]0.45x + 0.95*139-0.95*x = 97.3[/tex]
[tex]0.45x + 132.05-0.95x = 97.3[/tex]
Collect Like Terms
[tex]0.45x -0.95x = 97.3-132.05[/tex]
[tex]-0.50x = -34.75[/tex]
Make x the subject
[tex]x = \frac{-34.75}{-0.50}[/tex]
[tex]x = 69.5[/tex]
Recall that:
[tex]y = 139 - x[/tex]
[tex]y = 139 - 69.5[/tex]
[tex]y = 69.5[/tex]
This implies that:
69.5 tons of Alloy 1 (of 45% silver) and 69.5 tons of Alloy 2 (of 95% silver) is needed to make 139 tons of 75% silver alloy
