Question

How many ounces of a silver alloy that costs $5.50 per ounce should be mixed with one that costs $7.00 per ounce to make a new 30 ounce alloy that costs $6.40 per ounce?

Answer 1

Answer:

135.73 ounces of a silver alloy that costs $5.50 per ounce should be mixed.

Step-by-step explanation:

Given:

A silver alloy that costs $5.50 per ounce should be mixed with one that costs $7.00 per ounce to make a new 30 ounce alloy that costs $6.40 per ounce.

Now, to find the ounces of silver alloy.

Let the silver costs $5.50 per ounce be $x.$

And the silver costs $7.00 per ounce be $y.$

So, the total ounce make a new alloy:

$x+y=30\\y=30-x$  ....(1)

Now, the total costs of silver alloy:

$5.50x+7y=6.4$

Putting the value of $y$ from equation (1) in the place of $y$ :

$5.50x+7(30-x)=6.4$

$5.50x+210-7x=6.4$

$-1.5x+210=6.4$

Subtracting both sides by 210 we get:

$-1.5x=-203.6$

Dividing both sides by -1.5 we get:

$x=135.73$

Therefore, 135.73 ounces of a silver alloy that costs $5.50 per ounce should be mixed.