To make 3 gallons of a 3% solution with a solute of 28 index, how many ounces of solute will you need?

To determine how many ounces of solute are required to make a 3-gallon solution at a 3% concentration, we can use the concept of solution concentration, which is based on the amount of solute relative to the total volume of solution.

First, convert the total volume from gallons to ounces since the final answer needs to be in ounces. There are 128 ounces in a gallon, so for 3 gallons:

3 gallons × 128 ounces/gallon = 384 ounces.

Next, to find how much of the solute is needed to create a 3% solution in this total volume, you multiply the total volume by the desired percentage:

384 ounces × 0.03 (3%) = 11.52 ounces of pure solute needed.

However, since the solute has an index of 28, which indicates the density or concentration of the solute, we need to adjust for that. In this context, the index refers to a solute that is 28% concentrated. To find out how much of this solute is needed to obtain 11.52 ounces of pure solute, we can calculate as follows:

Let ( x ) be the amount of 28% solute needed. Since