s by blending together a​ quality bean costing ​$5.00 per pound and a cheaper bean at ​$2.00. nearest​ pound, find how much​ high-quality coffee bean and how much cheaper coffee bean she should blend.

Answer 1

you want x pounds of $y mixture

2<y<5

5T+2(x-T)=xy

3T=xy-2x

T=x(y-2)/3 lbs of $5

x-T= x-x(y-2)/3 lbs of $2

let y=$3.50 x=100 lbs

then T=50 lbs

x-T= 50 lbs

let y=$4, x=100 lbs

then

T=66 2/3 lbs

x-T= 33 1/3 lbs

5-4=1

4-2=2

4/2 =2 = 2 times as much $5 as $2

66 2/3 is twice 33 1/3

T/(x-T)=(y-2)/(5-y)