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?
A.
5.71 ounces
B.
7.00 ounces
C.
14.29 ounces
D.
13.00 ounces

Question

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?
A.
5.71 ounces
B.
7.00 ounces
C.
14.29 ounces
D.
13.00 ounces

whpalmer4 · Answer

Mixture problems like these are usually easy to solve if you focus on the amount of the substance, rather than the percentage.

If Tina wants a 20 oz gold necklace of 90% pure gold, the necklace will contain 90%*20oz = 0.90*20oz = 18 oz of gold.

The 75% pure gold contains 0.75 oz of gold per 1 oz.
The 96% pure gold contains 0.96 oz of gold per 1 oz.

The 75% and the 96% together must total 20 oz.

If you let L be the low grade (75%) gold and H be the high grade (96%) gold, then we have the following equations:

H+L = 20
0.96*H + 0.75*L = 18

Solve that system of equations for H and choose your answer accordingly.