Tina would like to melt down her existing gold jewelry to make a 20 ounce gold necklace that is 90% pure gold. After melting her jewelry, she is left with two batches. One batch is 75% pure. The other batch is 96% pure. How much of the 96% pure melted gold should Tina mix with the 75% pure melted gold to obtain 20 ounces of 90% pure gold?
Represent the amount of 96% and 75% pure gold by x and y, respectively. With the representation, the useful equations would be,
x + y = 20
0.96x + 0.75y = (20)(0.90)
The solution of this system of linear equation is (14.29, 5.71). Therefore, the amount of the 96% pure gold is 14.29 ounces. The answer would be letter C.