A local store sells two types of coffee beans: Arabica and Robusta. On Monday, the store s… — SAT

A local store sells two types of coffee beans: Arabica and Robusta. On Monday, the store sold $8$ pounds of Arabica coffee and $5$ pounds of Robusta coffee for a total of $\$62.00$ . On Tuesday, the store sold $4$ pounds of Arabica coffee and $7$ pounds of Robusta coffee for a total of $\$58.00$ . What is the cost, in dollars, of one pound of Robusta coffee?

Cevap: 6 dollars

Cevap

The cost of one pound of Robusta coffee is 6 dollars.

The correct answer is 6. By setting up the system of equations

8a + 5r = 62

and

4a + 7r = 58

, we can multiply the second equation by 2 to get

8a + 14r = 116

. Subtracting the first equation from this yields

9r = 54

, which simplifies to

r = 6

Adım Adım Çözüm

Define variables for the price per pound of Arabica coffee (

a

) and Robusta coffee (

r

), then set up a system of linear equations based on the given store sales information.

Equation 1:

8a + 5r = 62

Equation 2:

4a + 7r = 58

This translates the word problem context into a solvable system of mathematical equations.

Multiply the second equation by

2

to make the coefficients of

a

equal in both equations.

8a + 14r = 116

This prepares the system for solving by the elimination method.

Subtract the first equation (

8a + 5r = 62

) from the new equation (

8a + 14r = 116

) to eliminate

a

and solve for

r

9r = 54

, which simplifies to

r = 6

Subtracting the equations eliminates one variable, leaving a single-variable equation that is easily solved.

Anahtar Kavram

Solving systems of two linear equations in two variables using the elimination method.

Tahmini Süre:1m 30s

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