Sarah Meeham blends coffee for​ Tasti-Delight. She needs to prepare 170 pounds of blended coffee beans selling for ​$3.79 per pound.

Question

She plans to do this by blending together a​ high-quality bean costing

​$5.25

per pound and a cheaper bean at

​$2.50

per pound. To the nearest​ pound, find how much​ high-quality coffee bean and how much cheaper coffee bean she should blend.

She should blend

lbs of high-quality beans.

Answer 1

Let X= weight of high-quality beans (lbs)

Let Y= weight of cheaper beans (lbs)

Since Sarah wants to produce a total of 170lbs of coffee to sell, the weight of high-quality beans and cheaper beans must equal the total amount.

X + Y = 170 [1]

The price of a pound of the mixed coffee will be the price of the high-quality beans multiplied by the weight of the high-quality beans used in the mixture, plus the price of the cheaper beans multiplied by the weight of the cheaper beans used in the mixture. This must sum to $3.79 per pound multiplied by 170 pounds:

5.25*X + 2.50 *Y = 644.3 [2]

Proceed by solving the system of linear equations.

Multiply equation [1] by $2.50:

2.50X + 2.50Y = 425 [3]

Subtract equation [3] from equation [2]:

5.25X - 2.50X +2.50Y - 2.50Y = 644.3- 425

2.75X= 219.3

X= 79.745 lbs

Sarah must use 79.745lbs of the high-quality beans