Question

A coffee shop plans to blend a coffee that sells for $12 per pound with coffee that sells for $9 per pound to produce a blend that sells for $10 per pound. How much of each should be used to produce 20 pounds of the new blend?

Answer 1

Answer:

20/3 pounds of coffee that costs $12 per pound  and 40/3 pounds  of coffee that costs $9 per pound are required

Step-by-step explanation:

Let x be the amount of coffee that costs $12 per pound

Cost of x amount of this type coffee = 12x

We are supposed to find How much of each should be used to produce 20 pounds of the new blend that costs $10 per pound

So, Amount of coffee required that costs $9 per pound = 20-x

Cost of (20-x) amount of this type of coffee = 9(20-x)

So, $12x+9(20-x)=10(20)\\12x+180-9x=200\\3x=20\\x=\frac{20}{3}$

Amount of coffee that costs $12 per pound required is$\frac{20}{3} pounds$

Amount of coffee that costs $9 per pound required = 20-x=$20-\frac{20}{3}=\frac{40}{3} pounds$

Hence 20/3 pounds of coffee that costs $12 per pound  and 40/3 pounds  of coffee that costs $9 per pound are required