math help plz

Question

Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 110 pounds of blended coffee beans selling for $4.32 per pound. She plans to do this by blending together a high-quality bean costing $5.00 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.

Answer 1

First, I'm going to calculate how much of each quality she needs per lb of final product:

Let x be the amount of high quality beans per lb of final product

Then (1-x) is the amount of low quality bean per lb of final product

$5.00*x + $2.50*(1-x) = $4.32

$2.50*x + $2.50 = $4.32

$2.50*x = $1.82

x = 0.728 lb

and: (1-x) = 0.272 lb

Since we need 110 lbs of final product, we simply multiply these values by 110:

80.08 lb high-quality beans

29.92 lb low-quality beans

 

Answer 2

Allegation:

 

HAVE      WANT      NEED

5.00........................1.82....

..............4.32..................

2.50.......................0.68.....

 

So, you need 1.82 parts of the $5.00 bean and 0.68 parts of the $2.50 bean for a total of 2.5 parts

2.5 parts = 110 pounds

1 part = 44 pounds

1.82 parts x 44 pd/part = 80.08 lbs of $5.00 beans