Question

Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the House blend with the Organic Free Trade blend, but always in the same proportion. Yesterday, you mixed 140 pounds of the House blend with 168 pounds of the Organic Free Trade blend. Today, there is 130 pounds of the House coffee left in stock. How many pounds of the Organic Free Trade coffee should you mix with it to get your secret blend?

Answer 1

The ratio House blend/Organic Free Trade blend is the same and must remain the same.

So, the proportion is:

$\frac{140}{168}=\frac{130}{x}$

Where x is the unknown amount of the Organic Free Trade blend.

So, from the proportion, we have:

$\begin{gathered} 140\cdot x=168\cdot130 \\ 140x=21840 \\ \frac{140x}{140}=\frac{21840}{140} \\ x=156 \end{gathered}$

Answer: 156 pounds of Organic Free Trade blend