Question

Emily the blacksmith blends one alloy of silver that is 45% silver and another that is 95% silver. To the nearest ton, how much of each alloy is needed to make 139 tons of a 70% silver alloy?

please answer​

Answer 1

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

Explanation:

Given

`Alloy\ 1 = 45\%`

`Alloy\ 2 = 95\%`

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:

`x + y = 139`

Make y the subject

`y = 139 - x`

The percentage of each needed is represented as:

`45\% * x + 95\% * y = 139`

`45\% * x + 95\% * y = 70\% * 139`

`0.45x + 0.95y = 0.70 * 139`

`0.45x + 0.95y = 97.3`

Substitute 139 - x for y in the above equations

`0.45x + 0.95*(139-x) = 97.3`

`0.45x + 0.95*139-0.95*x = 97.3`

`0.45x + 132.05-0.95x = 97.3`

Collect Like Terms

`0.45x -0.95x = 97.3-132.05`

`-0.50x = -34.75`

Make x the subject

`x = (-34.75)/(-0.50)`

`x = 69.5`

Recall that:

`y = 139 - x`

`y = 139 - 69.5`

`y = 69.5`

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