Questions: Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Tanzanian blend with the Breakfast blend, but always in the same proportion. Yesterday, you mixed 90 pounds of the Tanzanian blend with 18 pounds of the Breakfast blend. Today, there is 30 pounds of the Tanzanian coffee left in stock. How many pounds of the Breakfast coffee should you mix with it to get your secret blend?

Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Tanzanian blend with the Breakfast blend, but always in the same proportion. Yesterday, you mixed 90 pounds of the Tanzanian blend with 18 pounds of the Breakfast blend. Today, there is 30 pounds of the Tanzanian coffee left in stock. How many pounds of the Breakfast coffee should you mix with it to get your secret blend?
Transcript text: Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Tanzanian blend with the Breakfast blend, but always in the same proportion. Yesterday, you mixed 90 pounds of the Tanzanian blend with 18 pounds of the Breakfast blend. Today, there is 30 pounds of the Tanzanian coffee left in stock. How many pounds of the Breakfast coffee should you mix with it to get your secret blend?
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Solution

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Solution Steps

Step 1: Calculate the ratio of the first blend to the second blend from the previous mixture

To maintain the same mixing ratio, we first calculate the ratio (R) from the previous mixture. The formula for the ratio is \(R = \frac{X_1}{Y_1}\), where \(X_1 = 90\) pounds and \(Y_1 = 18\) pounds. Substituting the values, we get \(R = \frac{90}{18} = 5\).

Step 2: Use the ratio to find the required amount of the second blend for today's mixture

Keeping the ratio constant, the formula to find the required amount of the second blend (\(Y_2\)) for today's mixture is \(Y_2 = \frac{X_2}{R}\), where \(X_2 = 30\) pounds. Substituting the values, we get \(Y_2 = \frac{30}{5} = 6\) pounds.

Final Answer:

To maintain the same mixing ratio, 6 pounds of the second blend should be mixed with 30 pounds of the first blend.

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