Question

Question #98ff2

Answer 1

The two numbers are :`23 1/3 and 38 1/3`

Or , `23.bar33 and 38.bar33`

Explanation:

Let the smaller number be `x`,
Given that: The difference of two numbers is 15.

So the other number will be `(x+15)` ------greater number.

Given that : half of the smaller number is greater than 1 upon 5 of the greater number by 4 . This can be written as:

`=> 1/2x = 1/5 xx (x+15) + 4`

`=> 1/2 x = x/5 +15/5 +4`

`=> 1/2 x = x/5 +cancel15^3/cancel5^1 +4`

`=> x/2 -x/5 = 3+4` ------transposition

`=> x/2 (5/5)-x/5(2/2) = 7`

`=> (5x -2x)/ 10 =7`

`=>3x= 7xx10`

`=> x= 70/3 = 23 1/3`

This is the smaller number.
So the greater number will be smaller +15:

`=> x+15 = 70/3 +15`

`=70/3 +15(3/3)`

`= (70+45)/3 = 115/3`

`= 38 1/3`

So, the two numbers are :`23 1/3 and 38 1/3`

Or `23.bar33 and 38.bar33`

We can cross check: difference = `38.33-28.33 =15`
and
`1/2 of 23.33 = 11.66` and `1/5 of 38.33 = 7.66`

`11.66` is greater than `7.66` by`4` ---same as given.