How many pounds of coffee worth $7 a pound should be added to 20 pounds of coffee worth $4 a pound to get a mixture worth $5 a pound?

Question

I don't understand how to solve such a problem. Any help is much appreciated!

Answer 1

Hi Phillip, 

Step One: Create Let Statement

Let x=pounds of coffee to be added

Step Two: Create an equation relating our let statement to the price values

5(x+20)=7x+4(20) Distribute

5x+100=7x+80 Rearrange

100-80=7x-5x Simplify

20=2x Divide both sides by 2

10=x

∴10 pounds of coffee worth $7 per pound should be added.

We can check our answer by plug in in our new value:

y(30)=7(10)+4(20) Distribute

y(30)=70+80 Combine like terms

y=150/30 Simplify

y=5

(Since we get five dollars, we know that our x=10 pounds is correct.)

Best, 
Star