Amy adds 15 ounces of orange powder to one jar of water to form concentrated orange juice. Then, she further uses that one jar of concentrated orange juice solution in 5 jars of water to prepare 24 gallons of diluted orange juice. How much orange powder is required to prepare the solution?

The initial recipe uses 15 ounces of orange powder and an unknown volume of water to create a concentrate, which is then mixed with 5 equal jars of water to create a total of 24 gallons. This means the final 24 gallons represents the initial water plus 5 identical jars of water, so the 15 ounces of powder is distributed across 6 total parts of water. To find the powder needed for the full 24 gallons, set up the proportion 15 ounces over 6 parts equals x ounces over 24 gallons. Solving for x gives (15 multiplied by 24) divided by 6, which equals 60 ounces of orange powder.

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