Finding all possible pairs of positive integer values

The ratio of the sum of two positive integers to their difference is $7:5$. If the the sum of the two numbers is at most $25$, find all possible values for the pair of numbers. Let $m$ be the first positive integer. Then $\frac{m}{6}$ is the second positive integer. This gives $m = 21.4$, but … Read more

If my salary grew from $1,200 a month to $1,300 a month, did I get $100/$1,200 = 8.3 % increase or $100/$1,300 = 7.7 % increase?

I’m math amateur. I was just given a raise at my job and my salary grew from $1,200 a month to $1,300 a month. I’m trying to figure out percentage growth in my salary. Did it grow $100$1,200=8.3% or did it grow $100$1,300=7.7% What’s the general rule for calculating percent growth when old value goes … Read more

Encoding 2 numbers into 1

Say we have two integers, a and b. I need a way to combine these numbers into one unique number x, such that they can both be recovered from x and no other numbers can be recovered from x There are plenty of ways to do this, but the problem is that I am using … Read more

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is $8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price SP of the phone, i.e. it’s Original Price OP (sale price excluding GST) + GST on it, is … Read more

Is there a way to encode all decimal numbers between 0 and 1 into whole numbers?

Is there a way to encode ALL decimal numbers between 0 and 1 into whole numbers with a rationale that supports sum operations between the encoded numbers? so 1=0.1 2=0.2 3=0.3… 1+2 = 3 .. 0.2+0.1 = 0.3 .. 3 = 0.3 But in way that we could theoretically include ALL decimal numbers between 0 … Read more

Question about a puzzle I am making up: lim\lim_{x\to \infty} \sqrt[x]{-1}

Me and my friends enjoy setting each other puzzles, and one that I have come up with recently is the following: \lim_{x\to \infty} \sqrt[x]{-1} My idea is that by thinking of rooting something as rotation in the complex plane (where you are halving the angle in polar coordinates with each root), you will find that … Read more