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?

Accepted Solution

Answer:18 poundsStep-by-step explanation:Quantity of Rift valley blend mixed = 90 poundsQuantity of Arabian Mocha blend = 27 poundsMixture proportion of  Rift valley blend : Arabian Mocha blend = 90 : 27 = 10 : 3This 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 poundsUsing constant proportion10 :3 is equivalent to 60: xUsing the law of ratio, we have3/10 =  x/60Cross multiplying both sides, we have:10x =180Dividing both sides by 10, we have:x = 180/10x = 18 poundsSo the quantity of Arabia Mocha to be used is 18 pounds.