Question

A coffee shop sells assorted types of coffees, and blends them into their "signature blends". Sri Lankan sells for $4.20 per pound, and Kona sells for $6.20 per pound. A customer pays $24.30 for 4 pounds of a blend. How much of each type of coffee goes into the blend?

Amount of Sri Lankan coffee =
pounds

Amount of Kona coffee =
pounds

Answer 1

The customer bought 0.25 pounds of Sri Lankan coffee and 3.75 pounds of Kona coffee

Data;

• Kona (y) = $6.20
• Sri Lankan (x) = $4.20

System of Equation

To solve this question, let us write a system of equations to show this problem.

$x + y = 4 ... equation (i)\\4.20x + 6.20y = 24.30... equation (ii)$

From equation (i)

$x + y = 4\\x = 4 - y...equation (iii)$

Put equation (iii) into equation (ii)

$4.20x + 6.20y = 24.30\\x = 4 - y\\4.20(4 - y)+ 6.20y = 24.30\\16.8 - 4.20y + 6.20y = 24.30\\16.8 +2y = 24.30\\2y = 24.30 - 16.80\\2y = 7.5\\2y/2 = 7.5/2\\y = 3.75$

Using the value of y which is the Kona's coffee, let's substitute this into equation (i) to solve for x

$x+y = 4\\x = 4 - 3.75\\x = 0.25$

From the calculations above,

• The amount of Sri Lankan coffee = 0.25 pound
• The amount of Kona coffee = 3.75 pounds

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