PLZ HELP WITH MATH QUESTION

Question

Katherine and Elijah are making customized jewelry for their clients. They use metal alloys with copper to design their products. Currently, they have an alloy that is 20% copper and an alloy that is 17% copper. They would like to mix the alloys to obtain 90 ounces of an alloy with 17.7% copper. How many ounces of each alloy must be mixed to obtain the desired alloy?

*MUST SHOW WORK FOR CREDIT*

Answer 1

I'll present two ways to solve this problem. For me, the first way (alligation) is the easiest, but not well known. You can google it to learn more. The second way is the more conventional algebraic way.

Method 1 (alligation)

HAVE........ WANT.......... NEED

20%..............................0.7 parts

..................17.7%......................

17%.............................2.3 parts

Total parts = 0.7 + 2.3 = 3 parts and this must equal the 90 ounces so each part = 90/3 = 30 ounces

0.7 parts of 20% = 0.7 x 30 parts = 21 ounces of the 20% alloy

2.3 part of 17% = 2.3 x30 = 69 ounces of the 17% alloy

Method 2 (algebra)

(x)(20) + (90-x)(17) = (90)(17.7)

20x + 1530 - 17x = 1593

3x = 63

x = 21 ounces of the 20% alloy

90-x = 69 ounces of the 17% alloy