Question

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 house blend, but always in the same proportion. yesterday, you mixed 100 pounds of the rift valley blend with 120 pounds of the house blend. today, there is 40 pounds of the rift valley coffee left in stock. how many pounds of the house coffee should you mix with it to get your secret blend?

Answer 1

To maintain the original mixing ratio of 5:6 (Rift Valley to House blend), 48 pounds of the House blend should be mixed with 40 pounds of the Rift Valley blend.

Step-by-step explanation:

You are dealing with a problem of proportions, where you want to mix two types of coffee blends in the same ratio as before. Previously, you mixed 100 pounds of the Rift Valley blend with 120 pounds of the House blend. This gives us a ratio of Rift Valley to House blend, which is 100:120 or reduced to 5:6 after dividing both numbers by 20. To find out how many pounds of the House blend to mix with 40 pounds of Rift Valley blend to maintain the same proportion, we can set up a proportion:

5/6 = 40/x

Where x is the amount of House coffee we need to find. Now, cross-multiply to solve for x:

5x = 40 * 6

x = 240 / 5

x = 48

Thus, you need to mix 48 pounds of House blend coffee with 40 pounds of the Rift Valley blend to maintain the same ratio and create the secret blend.