# The first number is 20% more than the second and 50% more than the third. How many percent

**The first number is 20% more than the second and 50% more than the third. How many percent is the second number greater than the third?**

According to the condition of the task, the first number is 20% more than the second and 50% more than the third. It is necessary to determine by what percentage the second number is greater than the third.

Let’s introduce unknown variables

let the first number X;

let the second number Y;

let the third number Z.

Let us express the first number in terms of the second

From the conditions of this task, you can make a proportion where the number Y is 100%, and the number X is (100 + 20) = 120%.

So X = 120 * Y: 100 = 120/100 * Y = 1.2Y.

Let us express the third number in terms of the second

From the conditions of this task, it is possible to compose the second proportion, where Z is 100%, and X = 1.2Y is (100 + 50) = 150%.

So Z = 1.2Y * 100: 150 = 120/150 * Y = 0.8Y.

Find the percentage of the second number greater than the third

So, we figured out that the third number is 0.8Y, and we entered the second number as Y.

This means that the proportion is obtained, where Y is 100%, you need to calculate how many percent is 0.8Y.

The solution to this proportion is the expression 0.8 * 100: 1 = 80%.

So the second number is greater than the third 100 – 80 = 20%.