A coffee merchant combines coffee that costs $5 per pound with coffee that costs $4.10 per pound. How many pounds of each should be used to make 27 lb of a blend costing $4.75 per pound?

Answer 1

Hi Mark B.

19.5 lbs of coffee at $5 per pound

7.50 lbs of coffee at $4.10 per pound

You can use a system of Equations and substitution

Let x = coffee at $5 per pound

Let y = coffee at $4.10 per pound

Equation 1 for total weight

x + y = 27

Note y = 27 - x

Equation 2 for total cost

5x + 4.10y = 4.75(27)

5x + 4.10y = 128.25

We can substitute 27 - x for y in Equation 2

5x + 4.10(27 - x) = 128.25

5x + 110.70 - 4.10x = 128.25

Combine like terms

5x - 4.10x + 110.70 = 128.25

0.90x + 110.70 = 128.25

Subtract 110.70 from both sides of the equation

0.90x = 17.55

Divide both sides by 0.90

x = 19.50

Since y = 27 - x

y = 27 - 19.50 = 7.50

Checking in both equations

19.50 + 7.50 = 27

27 = 27

5(19.50) + 4.10(7.50) = 128 .25

97.5 + 30.75 = 128.25

128.25 = 128.25

I hope this helps