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

To find the number of ounces of each silver alloy that should be mixed, we can use the concept of weighted averages.

Let's assume that x ounces of the silver alloy costing $3.50 per ounce are mixed with (30 - x) ounces of the silver alloy costing $7.00 per ounce to make a 30-ounce alloy costing $6.30 per ounce.

The total cost of the mixed alloy is equal to the sum of the costs of the individual alloys. So, we can write the equation:

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

Let's solve this equation to find the value of x:

3.50x + 210 - 7x = 189

Combine like terms:

-3.50x = 189 - 210

-3.50x = -21

Divide both sides by -3.50 to solve for x:

x = -21 / -3.50

x = 6

Therefore, the jeweler should mix 6 ounces of the silver alloy costing $3.50 per ounce with (30 - 6) = 24 ounces of the silver alloy costing $7.00 per ounce to make a 30-ounce alloy that costs $6.30 per ounce.