A jeweler wants to make a silver alloy to be used to make necklaces. How many ounces of a silver alloy that costs $3.50 per ounce should be mixed with one that costs $7.00 per ounce to make a new 30-ounce alloy that costs $6.30 per ounce

X oz. @ $3.50/oz.

(30-X) oz. @ $7.00/oz.

3.50x + 7.00(30-x) = 6.30*30
3.5x + 210 - 7x = 189
-3.5x = 189 - 210 = -21
X = 6 oz. @ 3.50/oz.
30-X = 30-6 = 24 oz. @ $7.00/oz.

To find the number of ounces of the silver alloy that costs $3.50 per ounce and the one that costs $7.00 per ounce that should be mixed to create a 30-ounce alloy costing $6.30 per ounce, we can use the method of equating the total cost before and after the mixing.

Let's assume x ounces of the $3.50 per ounce silver alloy are mixed and (30 - x) ounces of the $7.00 per ounce silver alloy are mixed.

The cost of the $3.50 per ounce silver alloy is 3.50 * x.
The cost of the $7.00 per ounce silver alloy is 7.00 * (30 - x).

The total cost of the new alloy, assuming it costs $6.30 per ounce, is (6.30 * 30).

Equating the total cost before and after mixing, we have the equation:

3.50 * x + 7.00 * (30 - x) = 6.30 * 30

Now we can proceed to solve this equation to find the value of x.

1. Distribute the terms:

3.50 * x + 210 - 7.00 * x = 189

2. Combine like terms:

-3.50 * x - 7.00 * x = 189 - 210

-10.50 * x = -21

3. Solve for x:

x = (-21) / (-10.50)

x = 2

Therefore, you will need 2 ounces of the $3.50 per ounce silver alloy and (30 - 2) = 28 ounces of the $7.00 per ounce silver alloy to create the new 30-ounce alloy that costs $6.30 per ounce.