Question

A distributor needs to blend a mix of Gualtemala Antigua coffee that normally sells for $8.50 per pound with a Rift Valley coffee that normally sells for $12.50 per pound to create 70 pounds of a coffee that can sell for $10.56 per pound. How many pounds of each kind of coffee should they mix?


A) Write an equation using the information as it is given above that can be solved to answer the question.
Use x as your variable to represent the quantity of Gualtemala Antigua coffee.
Equation: ____________________________________________________

B) (Round your answers to the nearest whole number of pounds.)
Answer: They must mix
___pounds of the Gualtemala Antigua coffee.
___pounds of the Rift Valley coffee.

Answer 1

9514 1404 393

Answer:

• x+y=70; 8.50x+12.50y=10.56(70)
• 36 pounds Antigua
• 34 pounds Rift

Step-by-step explanation:

At the insistence of the problem author, we will let x represent pounds of Antigua coffee and y represent pounds of Rift coffee. Then we have ...

  x + y = 70

  8.50x +12.50y = 10.56(70) . . . . . total cost of the mix

__

We like to use the variable to represent the high-cost contributor. Here, that is y, so we'll substitute for x:

  x = 70-y

  8.50(70 -y) +12.50y = 10.56(70)

__

  595 +4y = 739.2 . . . . . . . . . . . . . . simplify

  4y = 144.2 . . . . . . . . . . . subtract 595

  y = 36.05 . . . . . . . divide by 4

  x = 70 -36.05 = 33.95

About 36 pounds of Rift Valley coffee and 34 pounds of Gualtemala Antigua coffee must be mixed.

_____

Additional comment

By letting the variable in our equation 8.50(70 -y) +12.50y = 10.56(70) represent the high-cost coffee, we ensure that the simplified equation will have a positive coefficient for the variable. This means we don't have to mess with negative numbers, so eliminating a common source of math errors.

The problem requirement that we use x for the low-cost contributor meant we introduced an extra equation that would not have been needed.