Mathematics: Acoffee merchants want to make 6 pounds of a blend of coffee costing five dollars per pound. the blend is made using a six dollar per pound grade coffee and a three dollar per pound grade of coffee. how many pounds of each of these grades should be used?

Acoffee merchants want to make 6 pounds of a blend

SillyEve

11.03.2022

We should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.

Step-by-step explanation:

The blend should,

Cost = $5

Weigh = 6 pounds.

Lets take the weight of $6 coffee as pounds

And lets take the weight of $3 coffee as pounds.

Lets write an equation for the weight of the blend,

x+y=6 <---------- 1st equation.

$\frac{6x+3y}{x+y} =5$

= 6x+3y=5x+5y

= x=2y <---------- 2nd equation

We can substitute to x in 1st equation from 2nd equation,

⇒ 2y+y=6

= 2y+y=6

= 3y=6

= y=2

We can substitute y value to 2nd equation to find x,

⇒ x=2y

= x=2*2 = x=4

Therefore, we should use 4 pounds of $6 coffee and 2 pounds of $3 coffee for the blend.

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