Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Rift Valley blend with the Arabian Mocha blend, but always in the same proportion. Yesterday, you mixed 90 pounds of the Rift Valley blend with 27 pounds of the Arabian Mocha blend. Today, there is 60 pounds of the Rift Valley coffee left in stock. How many pounds of the Arabian Mocha coffee should you mix with it to get your secret blend?

18 pounds

Step-by-step explanation:

Quantity of Rift valley blend mixed = 90 pounds

Quantity of Arabian Mocha blend = 27 pounds

Mixture proportion of Rift valley blend : Arabian Mocha blend

= 90 : 27

= 10 : 3

This implies that for every 10 pounds of Rift Valley blend, we mix 3 pounds of Arabian Mocha.

So since the proportion is constant for the secret blend the let the unknown quantity of Arabian Mocha be "x" while the Rift Valley quantity be 60 pounds

Using constant proportion

10 : 3 is equivalent to 60: x

Using the law of ratio, we have

3/10 = x/60

Cross multiplying both sides, we have:

10x = 180

Dividing both sides by 10, we have:

x = 180/10

x = 18 pounds

So the quantity of Arabia Mocha to be used is 18 pounds.