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

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

$Alloy\ 1 = 45\%$

$Alloy\ 2 = 95\%$

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

$x = \frac{-34.75}{-0.50}$

$x = 69.5$

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