word problem help

Question

Sarah blends coffee. She needs to prepare 170 pounds of blended coffee beans selling for $4.12 per pound. she plans to do this by blending a high quality bean costing $5.25 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. 

Answer 1

h = pounds of high quality coffee

 

l = pounds of low quality coffee

 

h + l = 170

 

In order for Sarah to make this blended coffee, she needs to make sure that the cost of the input equals the cost of the output.

 

5.25h + 2.50l = 4.12 * 170

 

5.25h + 2.50l = 700.4

      h + l = 170

 

Multiply the second equation by 2.5. You get:

 

5.25h + 2.50l = 700.4

2.50h + 2.50l = 425

 

Subtract the second equation from the first. You get:

 

2.75h = 275.4

 

h = 100

 

l = 70

 

Sarah needs about 100 lb of high quality coffee & 70 lb. of low quality coffee for her blend.