Final answer:
To find the ratio of w to x, start by expressing y as 1.20x since y is 20% greater than x. Then, express w as 0.80y, and subsequently substitute the expression for y to get w as 0.96x. Finally, simplify the ratio 0.96:1 to its simplest form, 24:25.
Step-by-step explanation:
Let's start by defining x and y according to the given information. If y is 20% greater than x, this can be written as y = x + 0.20x or y = 1.20x. Next, if w is 20% less than y, then w = y - 0.20y or w = 0.80y. Substituting the expression for y into w gives us w = 0.80(1.20x) or w = 0.96x.
To find the ratio w : x in its simplest form, we divide w by x which results in w/x = 0.96x/x = 0.96. The ratio of w to x is thus 0.96 : 1, which can also be represented as 96 : 100 when scaled up to whole numbers. To simplify it, we divide both sides by 4, leading to the simplest form which is 24 : 25.