# GMAT Mixture Problems in Math

A coffee shop sells two types of coffee beans: Arabica and Robusta. Arabica beans cost $10 per pound, while Robusta beans cost $8 per pound. If a blend of Arabica and Robusta beans, totaling 20 pounds, is sold for $9 per pound, how many pounds of each type were used in the blend?

Question:

What is the weight of Arabica beans and Robusta beans used in the blend respectively?

Answer:

Let ( x ) represent the weight of Arabica beans (in pounds) and ( y ) represent the weight of Robusta beans (in pounds) used in the blend.

Given:

1. Total weight of the blend is 20 pounds: ( x + y = 20 )

2. Cost per pound of the blend is $9: ( 10x + 8y = 9 times 20 )

Solving the system of equations:

From equation (1): ( x = 20 – y )

Substituting ( x ) into equation (2):

[ 10(20 – y) + 8y = 9 times 20 ]

[ 200 – 10y + 8y = 180 ]

[ 200 – 2y = 180 ]

[ -2y = 180 – 200 ]

[ -2y = -20 ]

[ y = 10 ]

So, ( y = 10 ) pounds of Robusta beans.

Substitute ( y = 10 ) into equation (1) to find ( x ):

[ x = 20 – 10 ]

[ x = 10 ]

So, ( x = 10 ) pounds of Arabica beans.

Explanation:

This problem requires setting up a system of equations based on the given information. The first equation represents the total weight of the blend, while the second equation relates the total cost of the blend to the cost of the individual types of beans. By solving this system of equations, you can find the weights of Arabica and Robusta beans used in the blend. In this case, 10 pounds of Arabica beans and 10 pounds of Robusta beans were used.

In the GMAT, one of the sections is the quantitative section, which tests the professional / candidate’s ability to test their problem solving, or apply problems, and how common and mixing problems appear in the Quantitative section of the GMAT. It is important that the candidate knows how to differentiate between them. In the Graduate Management Admission Test exam, a common thing that falls and causes headaches to professionals who have already obtained good scores are quantitative questions.

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