Question

Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 140 pounds of blended coffee beans selling for 5.57 per pound. She plans to do this by blending together a high-quality bean costing $6.50 per pound and a cheaper bean at $3.25 per pound. To the nearest pound find how much high-quality coffee bean and how much cheaper coffee bean she should blend.

A) High-quality bean: 55 pounds, Cheaper bean: 85 pounds
B) High-quality bean: 70 pounds, Cheaper bean: 70 pounds
C) High-quality bean: 80 pounds, Cheaper bean: 60 pounds
D) High-quality bean: 90 pounds, Cheaper bean: 50 pounds

Answer 1

Sarah should blend 100 pounds of high-quality beans at $6.50 per pound and 40 pounds of cheaper beans at $3.25 per pound to create 140 pounds of a blended coffee that costs $5.57 per pound.

Step-by-step explanation:

Sarah Meeham needs to blend two types of coffee beans to create 140 pounds of a blend that costs $5.57 per pound. The high-quality beans cost $6.50 per pound, and cheaper beans cost $3.25 per pound. We need to find out how many pounds of each type of bean Sarah should use to achieve this price point for the final blend.

Let's call the amount of high-quality beans x pounds and the cheaper beans (140 - x) pounds. The total cost of x pounds of the high-quality bean is 6.50x dollars, and the cost of the cheaper beans is 3.25(140 - x) dollars. The combined cost of the beans should equal the cost of the finished blend, which is 5.57 * 140 dollars.

Using these equations, we set up the following:
6.50x + 3.25(140 - x) = 5.57 * 140

Solving the equation gives us:
6.50x + 455 - 3.25x = 779.8
3.25x + 455 = 779.8
3.25x = 779.8 - 455
3.25x = 324.8
x = 100 pounds

Therefore, Sarah should blend 100 pounds of high-quality beans. To find the amount of cheaper beans, we subtract this from the total weight:
140 - 100 = 40 pounds

So, Sarah should blend 100 pounds of high-quality beans and 40 pounds of cheaper beans.