Question

Sarah Meeham blends coffee for​ Tasti-Delight. She needs to prepare 130130 pounds of blended coffee beans selling for ​$4.734.73 per pound. She plans to do this by blending together a​ high-quality bean costing ​$6.006.00 per pound and a cheaper bean at ​$3.253.25 per pound. To the nearest​ pound, find how much​ high-quality coffee bean and how much cheaper coffee bean she should blend.

Answer 1

70 pounds of high-quality coffee bean and 60 pounds of cheaper coffee bean.

Explanation:

Total coffee weight = 130 pounds

Blend Cost = $4.73

High quality bean (H) price = $6.00

Cheaper bean (C) price = $3.25

The weight used of both beans must add up to 130 pounds, while the products of each individual quantity by its cost must add to 4.73 multiplied by 130.

`H+C=130\\6.00H + 3.25C= 130* 4.73`

Multiplying the first equation by -3.25 and adding it to the second one:

`6.00H - 3.25H + 3.25C - 3.25C = (130* 4.73) - (130*3.25)\\2.75H = 192.4\\H = 70\\C = 130 - H = 130 - 70\\C = 60`

Sarah should use 70 pounds of high-quality coffee bean and 60 pounds of cheaper coffee bean.