PSAT Math Multiple-Choice Question 23: Answer and Explanation

Question: 23

Laura has a recipe for cake that calls for both eggs and cups of flour. Laura can purchase five eggs and four cups of flour for $5.50 and nine eggs and eight cups of flour for $10.50. Based on these costs, what is the cost of the ten eggs that Laura will need for her recipe?

• A. $5.00
• B. $5.50
• C. $7.50
• D. $10.50

Correct Answer: A

Explanation:

A

The question asks for the cost of ten eggs. Translate the English into math to create a system of equations, and then solve the equations to find the price of eggs. The first purchase can be written as 5e + 4f = 5.50. The second purchase can be written as 9e + 8f = 10.50. Multiply the first equation by -2 to get -10e - 8f = -11.00, stack the equations, and add.

Therefore, e = 0.50. Multiply 0.50 by 10 to find the price of 10 eggs, which is $5.00. The correct answer is (A).