There are three numbers in the ratio of 3:5:7 and the sum of these numbers is…

Concept

In a ratio a:b:c, write the quantities as ax, bx, and cx. Their total is (a+b+c)x, so one ratio part equals the total divided by a+b+c.

Application

1. Let the three numbers be 3x, 5x, and 7x.

2. Their sum gives 3x + 5x + 7x = 975, so 15x = 975.

3. Therefore x = 975 / 15 = 65.

4. The numbers are 3×65 = 195, 5×65 = 325, and 7×65 = 455.

Cross-check

Their sum is 195 + 325 + 455 = 975, and dividing all three numbers by 65 gives 3:5:7.

Result

Hence, the three numbers are 195, 325, and 455.