She should blend ___lbs of high quality beans.

Question

she Needs to prepare 170 lbs of blended coffee beans selling for $4.71 per pound. She plans to do this by blending together a high-quality bean coating $6.00 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.

Answer 1

She wants to end with a mixture of 170 pounds of beans worth $4.71 per pound

the cheaper bean is worth $3.25 per pound TOTAL weight is 170 pounds, so we can let this one = x

the pricier bean is worth $6 per pound Its weight will be whatever # pounds remain from 170 so 170-x

basic concept is:

price * weight + price * weight + .... = price * total weight (* represents multiplication)

$6 (170 -x ) + $3.25 (x) = $4.71 (170) distribute and simplify

x = 79.745 rounded to 80 pounds cheaper coffee

170 - x = 170-80 = 90 pounds pricier coffee

CHECK : $6 (90) + $3.25 ( 80) = $800 due to rounding