I started with one hexagon, then kept drawing larger and larger hexagons. I must be really bored because I found myself wondering how many dots I would have altogether after the fiftieth hexagon. What’s the answer?

Achemist has 200 ml of a 10% sucrose solution. she adds x ml of a 40% sucrose solution. the percent concentration, y, of the final mixture is given by the rational function: the chemist needs the concentration of the final mixture to be 30%. how many milliliters of the 40% solution should she add to the 10% solution to get this concentration?