Answer:
18, 24, 30
Explanation:
Here are two methods of solving this problem.
1)
We can do this by trial and error.
The ratio needs to be 3:4:5 with a sum of 72.
Try 3 + 4 + 5 = 12. That is way too small.
Multiply each number by 4:
4 * 3 = 12
4 * 4 = 16
4 * 5 = 20
Now add the products: 12 + 16 + 20 = 56. That is closer.
Try multiplying the numbers in the ratio by 6.
6 * 3 = 18
6 * 4 = 24
6 * 5 = 30
Add the products: 18 + 24 + 30 = 72
That is the answer.
Answer: 18, 24, 30
2)
We can do this with an equation.
We know we need to multiply the three numbers in the ratio by a number, but we don't know what that number is. Let's call the multiplier x.
The numbers in the ratio become
3x
4x
5x
We want their sum to be 72.
3x + 4x + 5x = 72
12x = 72
x = 72/12
x = 6
Now we know the multiplier is 6.
6 * 3 = 18
6 * 4 = 24
6 * 5 = 30
Answer: 18, 24, 30