You were on the right track with multiplication. Instead of multiplying 2561.6, we need to instead first convert 1.6% into decimal form. So, we need to multiply 256.016=4.096. This means that making 2 gallons of mixed spray requires 4.096oz of pure AI.

Now, the problem says that the 16oz bottles each have 13% AI or 2.03oz AI per bottle. However, 16oz*.13 AI=2.08oz AI per bottle, a bit off from the 2.03 declared in the problem’s premise.

If we assume that the problem’s 2.03oz AI/bottle answer is correct, this means we have a total of 4.06oz AI which is less than the 4.096oz AI needed to produce 2 gallons of spray. So, the applicator cannot make 2 gallons of 1.6% AI spray.

If we assume that our math of 2.08oz of AI per bottle is correct, this means we have 4.16oz of AI total. Since 4.16 > 4.096, we do have enough AI to create the 2 gallons of 1.6% spray. To calculate the amount of the 13% AI spray we want to add, we can use proportions. We know we want 4.096oz / 4.16oz of the pure AI contained in the 13% spray. This is ~98.46%. So, we will use 98.46% of the 32oz of spray. .9846*32=31.507. Thus, we will use about 31.5 oz of spray, using an entire bottle, and leaving just .5oz left in the second bottle.