The sum of two numbers is 100 and their ratio is 2:3. What is the larger number?

To find the larger number when the sum of two numbers is 100 and their ratio is 2:3, we start by letting the two numbers be represented as 2x and 3x, based on the given ratio.

The equation for the sum of these two numbers can be set up as follows:

2x + 3x = 100

Combining the terms on the left side gives:

5x = 100

Next, we solve for x by dividing both sides by 5:

x = 20

Now that we have the value of x, we can determine the two numbers. The first number, which corresponds to 2x, is:

2x = 2 * 20 = 40

The second number, which corresponds to 3x, is:

3x = 3 * 20 = 60

Since the question asks for the larger number, we see that 60 is indeed greater than 40. Therefore, the larger number in this case is 60. This method highlights how ratios can be efficiently utilized to solve problems involving sums and relationships between two numbers.