Question

I thought of a number, I added 1 3 4 to it, then I multiplied the result by 2 2 11 and I got 8. What was my number?

Answer 1

Question:

I thought of a number, I added 1 3/4 to it, then I multiplied the result by 2 2/11 and I got 8. What was my number?

Answer:

The number is
`1(11)/(12)`

Explanation:

Let the number be x.

Analyzing the steps, 1 at a time

Add
`1(3)/(4)` to x

This implies:

`x + 1(3)/(4)`

Multiply by
`2(2)/(11)` to result in 8

This implies:

`(x + 1(3)/(4)) * 2(2)/(11) = 8`

Now, we solve for x

Convert mixed numbers to improper fractions

`(x + (7)/(4)) * (24)/(11) = 8`

`((4x + 7)/(4)) * (24)/(11) = 8`

Multiply through by 11

`11 * ((4x + 7)/(4)) * (24)/(11) = 8 * 11`

`((4x + 7)/(4)) * 24 = 88`

Divide through by 24

`((4x + 7)/(4)) * 24/24 = 88/24`

`(4x + 7)/(4) = (88)/(24)`

Multiply through by 4

`4 * (4x + 7)/(4) = (88)/(24) * 4`

`4x + 7 = (88 * 4)/(24)`

`4x + 7 = (88)/(6)`

`4x + 7 = (44)/(3)`

Make 4x the subject

`4x = (44)/(3) -7`

`4x = (44-21)/(3)`

`4x = (23)/(3)`

Solve for x

`x = (23)/(3 * 4)`

`x = (23)/(12)`

`x = 1(11)/(12)`

Hence, the number is
`1(11)/(12)`