word problem

Question

A coffee merchant wants to make 30 lb of a blend of coffee costing $4.80 per pound. The blend is made using a $6.00 grade and a $4.00 grade of coffee. How many pounds of each grade of coffee should be used?

Answer 1

Let H = the amt of high priced coffee and L = the amt of lower priced coffee

H + L = the total amt of coffee to be made = 30

6H = the cost of the higher priced coffee and 4L = the cost of the lower priced coffee

4.80*30 = the cost of the final amt of mixed coffee

6H + 4L = 4.8*30 => 3H + 2L =72

 

H + L = 30

3H + 2L = 72

 

Multiply the first equation by 2 and subtract it from the 2nd equation

2H + 2L = 60

3H + 2L = 72

H = 12 and then L = 30 - H = 18

 

You should take these two answers and check that they meet the stipulations in the question.