Find the sum of three numbers knowing that the first refers to the third as 3 3/4: 4 1/2 the second refers

Find the sum of three numbers knowing that the first refers to the third as 3 3/4: 4 1/2 the second refers to the third as 5: 2 and the sum of the first and the second is 500.

From the fact that the second number is related to the third as 5: 2, we can conclude that the second number is 2.5 times larger than the third. Then the ratio of the first to the second will be 3.75: (4.5 * 2.5) or 3.75: 11.25.

Let’s make a proportion – the sum of the first two numbers relates to the sum of its relative weights as the third number to its relative weight:
500 / (3.75 + 11.25) / 500 = x / 4.5;
500/15 = x / 4.5;
x = (4.5 * 500) / 15 = 150.

Answer: The sum of three numbers is 500 + 150 = 650.

Note. You can find that the first two numbers are 125 and 375.