Algebra 1b unit 4

Question

You decide to make your own hand sanitizer to sell on Etsy. In your garage you find 5 quarts of some antiseptic counter cleaner that is a solution of alcohol and water. The label says it’s 40% alcohol, which is too strong for skin.  To weaken the solution to 25% alcohol, how much water will you have to add and how much total solution will you have in the end? If you sell it in 4 oz. bottles for $4.95 per bottle, how much will you earn from your sales?

Find your answer using a chart. Include the chart and your explanation about whether or not your answers is reasonable.

PLEASE HELP.....

Answer 1

Hello, Serena,

To make a 25% solution from a 40% solution, we'll need to add water. How much can be determined with the following relationship.

40% is 40/100. We want to add x volume to the 100 so that the ratio becomes 25%, or 25/100. That can be written as:

40/(100+x) = 25/100

Solve for x and you'll find that x = 60. Try adding 60 volume units to see if we get 25%

40/(100+60) = 40/160 = 25%

So for every 100 units of the 40% alcohol solution, we need to add 60 units of water to get a 25% solution. This can also be stated as "we need to increase the total volume by 60% to achieve a 25% alcohol solution."

If we have 5 quarts, we'll need to add 5*0.60 quarts, or 3 quarts of water. That would give us a total of 8 quarts of 25% alcohol.

One quart is 160 ounces. So convert to ounces:

(160 oz/quart)*(8 quarts)= 1280 oz

We sell 4oz for $4.95. We'll make that a conversion factor: $4.95/4oz

Multiply the total ounces by the conversion factor to get total $, assuming all is sold:

1280oz*($4.95/4oz) = $1584

I'm not sure what you can put into a chart, except, perhaps, for revenue as a function of 4oz units sold.

Bob