Question

A company is going to mix two kinds of coffee. The brand X

costs $7 per pound. The brand Y costs $4 per pound. The
company wants 90 pounds worth $540.
Write a system of equations. How much of brand X should it
use?

Answer 1

To determine the amount of brand X coffee to use, we set up a system of equations based on the given prices and total desired value. By solving the system, we find that the company needs 60 pounds of brand X coffee.

Step-by-step explanation:

The company needs to mix two kinds of coffee, brand X costing $7 per pound and brand Y costing $4 per pound, to make a blend worth $540 for 90 pounds. We can create a system of equations to determine how much of each brand the company should use.

Step 1: Define the variables

Let x represent the number of pounds of brand X and y represent the number of pounds of brand Y.

Step 2: Write the equations

The first equation represents the total weight:

x + y = 90

The second equation represents the total cost:

7x + 4y = 540

Step 3: Solve the system of equations

Using substitution or elimination, we find the values of x and y.

For example, by multiplying the first equation by 4 and subtracting it from the second equation, we can solve for x:

(7x + 4y) - (4x + 4y) = 540 - 360
3x = 180
x = 60

Therefore, the company should use 60 pounds of brand X.