Question

At The Old Home Fill'er Up and Keep on a-Truckin' Cafe, Mavis mixes two different types of coffee beans to produce a house blend. The first type costs $2 per pound and the second costs $7 per pound.
How much of each type does mavis use to make 75 pounds of a blend which costs $4 per pound?

Answer 1

There are 45 pounds and 30 pounds of each type respectively.

Step-by-step explanation:

Since we have given that

Cost of first type = $2 per pound

Cost of second type = $7 per pound

Cost of mixture = $4 per pound

So, we need to find the quantity of each type to make 75 pounds of a blend.

We will use "Mixture and Allegations":

  First type         Second type

       2                         7

                     4

---------------------------------------------------

     7  - 4       :              4 - 2

      3             :                2

So, Quantity of first type would be

$\dfrac{3}{5}\times 75=3\times 15=45\ pounds$

Quantity of second type would be

$\dfrac{2}{5}\times 75=2\times 15=30\ pounds$

Hence, there are 45 pounds and 30 pounds of each type respectively.