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