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## Ask Professor Puzzler

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Question: "If I’ve used ninety percent of my hand sanitizer which was seventy percent alcohol, and I refill the bottle with new hand sanitizer which is eighty percent alcohol, what is the new alcohol content of the bottle?"

This is a fairly straightfoward mixture problem. One way of approaching this problem is to begin by writing everything as a percent:

Initailly, the bottle of hand sanitizer was 100% full, then 90% was removed. Thus, we had 100% - 90% = 10%. And 70% of that was alcohol.

Then we filled the container back up, meaning we added (100% - 10%) = 90%. And 80% of that was alcohol.

Thus, the amount of alcohol in the mixture is
10% x 70% + 90% x 80% =
0.10 x 0.70 + 0.90 x 0.80 =
0.07 + 0.72 = 0.79 =
79%

NOTE: If you want to practice doing word problems, the lesson plans section of the site contains a page on mixture word problems. There are worksheets available, and answer keys for pro members.

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