Why is this the answer to my math word problem?

Question

A blend of coffe is made by mixing Comombian coffee at $8 a pound with espresso coffe at $3 a pound. If the blend is worth $5 a pound, how many pounds of the Colombian coffe are neeeded to make 50 pounds of the blend?

Answer is 20

Answer 1

Set it up using algebra, as a system of two equations:

Let weight of Columbian coffee be x, and of expresso be y.

Then use the facts given to make two equations.

We know total weight is 50 lbs, so x + y = 50.

We also know coffee should be worth $5 a pound, so total cost should be 5 x 50 = $250.  

So 8x + 3y = 250

Now there are two equations:

8x + 3y = 250

x + y = 50

Multiply second equation by -3 and add:

8x + 3y = 250

-3x -3y = -150

5x = 100

x = 20

So y = 30

Answer 2

answer is 1

Answer 3

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