MATH SOLVE

2 months ago

Q:
# A metal alloy is a metal made by blending 2 or more types of metal. A jeweler has supplies of two metal alloys. One alloy is 30% gold and the other is 10% gold. How much of each alloy should the jeweler combine to create 4 kg of an alloy containing 15% gold?

Accepted Solution

A:

Answer:1 kg of 30% gold and 3 kg of 10% goldStep-by-step explanation:Let us take "x" kg of 30% gold, and"y" kg of 10% goldWe need to make 4 kg of 15% gold, that would be:4(15%) = 4 (15/100) = 4(0.15) = 0.6kgWe can now write an equation as:30%x + 10%y = 4(0.15)0.3x + 0.1y = 0.6 (equation 1)Also, we know there will be 4 kg from "x" and "y", so we can write:x Β + y = 4or x = 4 - yWe substitute this into equation 1 and solve for y first:0.3x + 0.1y = 0.60.3(4 - y) + 0.1y = 0.61.2 - 0.3y + 0.1y = 0.60.2y = 0.6y = 3And x = 4 - y, x = 4 - 3 = 1So, 1 kg of 30% gold and 3 kg of 10% gold