Question

Three numbers whose sum is `54` are such that one is double another and triple the other. What are the three numbers?

Answer 1

9, 18, 27

Explanation:

Let the unknown numbers be a, b, c where `a < b < c`

The question is not explicit enough to have no doubt about all the relationships.

No doubt about this one: `" "a+b+c=54`

Assumption

`b=2a`
`c=3a`

`a" "+" "b" "+" "c" "=54`
`darr" "darr" "darr`
`a" "2a" "3a" "=54`

`=> 6a=54`

Divide both sides by 6

`6/6a=54/6=9`

`color(blue)(a" "=" "color(white)(2)9)`
`color(blue)(b=2a=" "18)`
`ul(color(blue)(c=3a=" "27) larr" add"`
`" "54`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose you meant

`b=2a`
`c=3b = 3(2a)=6a`

Then proceed using the same approach as the solution above.

Answer 2

`324/11`, `162/11`, `108/11`

Explanation:

I suspect that the question is incorrectly posed. For example, if two of the numbers were respectively double and triple the other number, then the numbers would be `9, 18, 27`.

With the question as posed, the three numbers take the form:

`x`, `x/2` and `x/3` for some constant `x` to be determined.

So their sum is:

`x+x/2+x/3 = (6x+3x+2x)/6 = (11x)/6 = 54`

Hence:

`x = (6*54)/11 = 324/11`

and the three numbers are:

`324/11`, `162/11`, `108/11`