Ants are keen scavengers bent on finding even the smallest of crumbs. Unfortunately for Orange and Grey, who don’t always clean up too well, their home is currently being flooded with ants. It’s time for some cleaning.
“So it looks like the best concentration of alcohol for cleaning is 70%, but we only have 91%. Should we buy some more?” Grey asked inquisitively.
“I have a better idea,” said Orange. “We can mix our own. After all, the 70% alcohol is just a more dilute form of the 91%.”
“Good thinking!” said Grey. “But it sounds pretty complicated to mix that. Let’s start by planning some things out.” The two cats quickly gathered some supplies and some scratch paper.
“So,” Orange announced, “we have a 10 fluid ounce bottle here that we will fill with a new 70% mixture.”
“The first step should be to find out how much alcohol we want in our finished product,” Grey declared. “Since we want 70% of our bottle to be alcohol, let’s find 70% of 10.”
Orange quickly scribbled an equation before adding, “In order to find that, let’s convert 70% to the decimal 0.7. Now, 0.7 x 10 = 7 fluid ounces of alcohol. So, now we need to find out how much of the 91% solution to add so we can get 7 fluid ounces of alcohol in the finished product.”
“That sounds really complicated!” Grey gasped. “How can we find that out?”
“Well let’s look at it step by step,” said Orange. “Let’s review what the 91% means. For every 100 units of the solution, 91 of those will be alcohol and the rest will be water. We just need to scale it down so that instead of 100 fluid ounces of solution with 91 being alcohol, we only have 7 .”
“I just realized! We can do the opposite process of what we just did in order to figure out how much 91% we need,” Grey exclaimed. “Instead of multiplying, we will divide 7 by 0.91. This gives us 7.692.”
Orange nodded. “So now, all we have to do is measure out 7.692 ounces of the 91% alcohol mix. If we fill in the rest of the solution with water, we will then have a 70% alcohol mix.”
“We should double check our work now,” Grey said. “Let’s check by finding out the amount of water in the solution this time. Since 70% of our finished solution is alcohol, the remaining 30% is water. 30% of 10 is 3, so we should have 3 fluid ounces of water.”
“Good idea,” Orange agreed. “It’s always good to double check your work to avoid accidents. So, we have added 7.692 fluid ounces of the 91% solution to our bottle. That means there is 10 – 7.692, or 2.308 fluid ounces of pure water added afterwards.”
“Let’s not forget about the water that is in the 91% mixture. Since 91% of it is alcohol, it is only 9% water. We can multiply 7.692 by 9% to find the amount of water from there,” Grey confirmed.
“Exactly,” Orange said, scrawling across the paper. “Now, 0.09 x 7.692 is 0.692. If we add 0.692 and 2.308, we will get 3. So it looks like our math was correct!”
After mixing their 70% alcohol solution, Orange and Grey began tirelessly scrubbing and cleaning. Finally, after hours of hard work, they removed all the traces of food and the ants began leaving.
“Lesson learned,” Grey commented. “It’s much easier to clean sooner rather than later.”
Disclaimer: These numbers may not be completely exact due to how chemical bonds form, but will be perfectly sufficient for all everyday needs.