Sarah Meeham blends coffee for Tasi-Delight. She needs to prepare 140 pounds for blended coffee beans selling for $5.07 per pound. She plans to do this by blending together a high-quality bean costing $6.50 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.

Question

Sarah Meeham blends coffee for Tasi-Delight. She needs to prepare 140 pounds for blended coffee beans selling for $5.07 per pound. She plans to do this by blending together a high-quality bean costing $6.50 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. (Round to the nearest pound as needed.)

Answer 1

If there are x lbs of $6.50 coffee, then the rest (140-x) of $2.50 beans. So, add up the total cost of the various amounts:

6.50x + 2.50(140-x) = 5.07(140)

Now just find x and then 140-x.

Answer 2

PLEASE HELP! THIS QUESTION INVOLVED

Answer 3

To find out how much high-quality coffee bean Sarah should blend, we can use a weighted average formula.

Let's assume that Sarah needs to blend x pounds of the high-quality bean.

The cost per pound of the high-quality bean is $6.50, and the cost per pound of the cheaper bean is $2.50. The total weight of the blended coffee should be 140 pounds.

To find the weighted average of the two beans, we can set up the following equation:

(6.50 * x) + (2.50 * (140 - x)) = 5.07 * 140

Let's solve for x:

6.50x + 2.50(140 - x) = 5.07 * 140

6.50x + 350 - 2.50x = 707.80

4x = 707.80 - 350

4x = 357.80

x = 357.80 / 4

x ≈ 89.45

To the nearest pound, Sarah should blend approximately 89 pounds of high-quality beans.