PSAT Math Multiple-Choice Question 556: Answer and Explanation

Question: 556

18-karat gold has 18 parts gold for 24 total parts metal (the difference comes from the 6 parts that are metals other than gold). 24-karat gold is pure gold. In order to make a piece of jewelry that is 2.4 ounces in weight and is 20-karat gold, how many ounces of 18-karat gold, X, and of 24-karat gold, Y, are needed to make this piece of jewelry

• A. X = 0.4, Y = 0.6
• B. X = 0.9, Y = 1.7
• C. X = 1.2, Y = 1.1
• D. X = 1.6, Y = 0.8

Correct Answer: D

Explanation:

(D) Set up a system of two equations. One equation models the number of actual gold -karats:

One equation models the weight of the jewelry:

X + Y = 2.4

You can use either substitution or elimination to solve this system. However, using elimination is better since a Y-term in each equation will be easily canceled. Start by simplifying the first equation:

Now subtract it from X + Y = 2.4:

Then solve for X:

Now plug in 1.6 for X into one of the equations to solve for Y. Use X + Y = 2.4 since it is simpler:

X + Y = 2.4

1.6 + Y = 2.4

Y = 0.8

So the final answer is X = 1.6, Y = 0.8.