Finding a number that reduces an alarm percentage below its threshold.

Question

I may be in the wrong place, but I have a consistent problem that I need a formula for, I can't even figure out what it's called. (AI could not help me.) It's nested in a computer issue, but I am asking about the math needed to solve the word problem:

I have an alarm that triggers when a hard drive reaches 80% capacity. The drive has a 320 GB hard drive. The drive is 88% full. What size of hard drive (in whole GB) do I need to bring the percent full value down to 75%?

I think it has to do with ratios, maybe? But I cannot figure out the correct way to set up the problem much less solve it. Two examples of my difficulties: If I am trying to set up a ratio equation, do I use the percentage or the number the percentage represents (320 * .88 = 281.6)? Or, in constructing the ratio, I am looking for what I think would be the bottom number on the right side, how do I get that to something like "x ="?

Thanks

Answer 1

You have $$320 \text{GB capacity} * .88 = 281.6\;\text{GB}$$ used at the current moment.

If you want your desired ratio to be $75\%$, we need $$.75 = \frac{\text{current GB used}}{\text{ new capacity}} \implies .75 = \frac{281.6 \text{ GB}}{\text{new capacity}} \implies \text{new capacity} = \frac{281.6 \text{ GB}}{.75} = 375\text{ GB}.$$

Answer 2

Your hard drive is 320GB and 88% full; so, right now, your hard drive has $320\cdot .88 = 281.6$ GB on it. You would like that to correspond to 75% of the full value. That is, you are looking for $x$ so that 75% of $x$ is $281.6$. Mathematically, $x\cdot .75 = 281.6$ or $x = 281.6/.75 \approx 375.5$.

So another 64GB of ram will have you covered!

PS: this website is usually for undergraduate level questions. Therefore, for questions like this, you will get an answer faster on a website geared towards a different (i.e. less math heavy) audience.