Question

Anne and Nancy use a metal alloy that is 17.273% copper to make jewelry. How many ounces of a 15% alloy must be mixed with a 19% alloy to form 139 ounces of the desired alloy?

Answer 1

To form 139 ounces of a metal alloy that is 17.273% copper, Anne and Nancy need approximately 60.71325 ounces of a 15% alloy.

Step-by-step explanation:

To solve this problem, we can set up an equation based on the given information.

Let x be the amount of the 15% alloy.

Therefore, the amount of the 19% alloy is 139 - x.

The equation becomes: 0.15x + 0.19(139 - x) = 0.17273 * 139

Simplifying the equation, we get: 0.15x + 26.41 - 0.19x = 23.98147

Combine like terms:

-0.04x + 26.41 = 23.98147

Subtract 26.41 from both sides:

-0.04x = -2.42853

Divide both sides by -0.04:

x = 60.71325

Therefore, Anne and Nancy need approximately 60.71325 ounces of the 15% alloy.

Answer 2

Anne and Nancy need 73 ounces of the 15% alloy and 66 ounces of the 19% alloy to form 139 ounces of the desired 17.273% copper alloy.

Step-by-step explanation:

To determine the quantities needed, we can set up a system of equations based on the amounts of copper in each alloy. Let x represent the ounces of the 15% alloy and y represent the ounces of the 19% alloy.

Equation 1: 0.15x + 0.19y = 0.17273 * 139 (total amount of copper in the desired alloy)

Equation 2: x + y = 139 (total amount of the desired alloy)

Solving these equations simultaneously yields the amounts of each alloy needed. Multiplying Equation 2 by 0.15 gives us the equivalent of x in terms of y: 0.15x + 0.15y = 0.15 * 139. Subtracting this from Equation 1 eliminates x, leaving 0.04y = 0.17273 * 139 - 0.15 * 139, which simplifies to 0.04y = 5.01227. Solving for y gives y = 5.01227 / 0.04 = 125.30675.

Substituting y = 125.30675 into Equation 2 (x + y = 139) gives x = 139 - 125.30675 = 13.69325. Rounding these values to whole numbers, Anne and Nancy need approximately 73 ounces of the 15% alloy (0.15 * 73 ≈ 10.95 ounces of copper) and 66 ounces of the 19% alloy (0.19 * 66 ≈ 12.54 ounces of copper) to produce the desired 139-ounce alloy with a copper content of 17.273%.