Question

How do you find the two numbers whose ratio is 3 to 4 and that have a sum of 35?

Answer 1

The two numbers are `{105/4, 35/4}`

Explanation:

Let the two numbers be `a` and `b` such that
[1]`color(white)("XXX")a/b=3`
and
[2]`color(white)("XXX")a+b=35`

From [1] (assuming this is a meaningful expression: `b!=0`)
we have
[3]`color(white)("XXX")a=3b`

Then substituting `3b` for `a` in [2]
[4]`color(white)("XXX")3b+b=35`
or
[5]`color(white)("XXX")b=35/4`

Combining [3] and [5]
[6]`color(white)("XXX")a=105/4`