I don't know how to begin this question

Question

an acrylic container holding 1.5 gallons can only hold a liquid with a maximum of 7% alcohol content otherwise the container will become scratched. Wishing to make sangria you must use two bottles of wine (25 ounces each) at 11% alcohol. How much seltzer water should you add to bring the sangria to the 7% threshold how much sangria have you made? can you make a double batch in the container? I went to math tutors at my university but they said they didn't understand the problem either

Answer 1

Hi Ruby,

First, we know we can't have more than 1.5 gallons in the container. Each gallon is 128 ounces, so our maximum volume in ounces is 128(1.5)=192 ounces.

We need the total solution to be a maximum of 7% alcohol.

Let w = ounces of 11% wine, 0.11w = ounces of alcohol

Let s = ounces of seltzer

The % of alcohol in the solution will be (ounces of alcohol)/(ounces of wine + seltzer) =(0.11w)/(w + s)

If both bottles of wine are totally used, then w = 50

We want (0.11)(50)/(50 + s) = 7% = 0.07

Solve for s. Hint: start by multiplying each side by (50 + s)

 

Jason