arah Meeham blends coffee for Tasti-Delight. She needs to prepare 120 pounds of blended coffee beans selling for $ 4.75 per pound. She plans to do this by blending together a high-quality bean costing $ 5.25per 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.

Question

arah Meeham blends coffee for​ Tasti-Delight.  She needs to prepare 120 pounds of blended coffee beans selling for ​$ 4.75 per pound.  She plans to do this by blending together a​ high-quality bean costing ​$ 5.25per 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.

R_scott · Accepted Answer

h + c = 120 ... 13 h + 13 c = 13 * 120 5.25 h + 3.25 c = 4.75 * 120 ... dividing by .25 ... 21 h + 13 c = 19 * 120 subtracting equations ... 8 h = 6 * 120 solve for h , then substitute back to find c

oobleck · Answer

If using x lbs of cheaper coffee, then 3.25x + 5.25(120-x) = 4.75*120 x=30, so 30 lbs cheap, 90 lbs expensive makes sense, since 4.75 is much closer to 5.25 than it is to 3.25

Explain Bot · Answer

To find how much high-quality coffee bean and cheaper coffee bean Sarah should blend, we can set up a system of equations. Let's assume she needs to blend x pounds of high-quality coffee bean and y pounds of cheaper coffee bean. According to the problem, she needs to prepare a total of 120 pounds of blended coffee beans. Therefore, we can write the first equation as: x + y = 120 Next, we know that the blended coffee beans will sell for $4.75 per pound. The cost of the high-quality coffee bean is $5.25 per pound, and the cheaper coffee bean is $3.25 per pound. So, the second equation can be written as: (5.25 * x) + (3.25 * y) = 4.75 * 120 Now, we can solve this system of equations. First, multiply the first equation by 3.25 to eliminate y: 3.25x + 3.25y = 3.25 * 120 Next, subtract the above equation from the second equation: (5.25 * x) + (3.25 * y) - (3.25x + 3.25y) = 4.75 * 120 - 3.25 * 120 This simplifies to: 5.25x - 3.25x = 570 - 390 2x = 180 Divide both sides by 2: x = 90 Now, substitute this value of x into the first equation to find y: 90 + y = 120 y = 120 - 90 y = 30 Therefore, Sarah should blend 90 pounds of high-quality coffee bean and 30 pounds of cheaper coffee bean. To summarize, Sarah should blend 90 pounds of high-quality coffee bean with 30 pounds of cheaper coffee bean to prepare 120 pounds of blended coffee beans.