One number is 1.5 times larger than the other. The arithmetic mean of these numbers is 37. Find the larger number.

Let the second number be x, then the first 1.5 * x. To find the arithmetic mean, you need to add the numbers and divide by their number.
(x + 1.5x) / 2 = 37
2.5x = 37 * 2
2.5 * x = 7.4
x = 74 / 2.5
x = 29.6
So the second number was 29.6, and the first:
29.6 * 1.5 = 44.4.
Answer: These numbers are 44.4 and 29.6.