Question

I thought of a number, divided it by 1 1/2 , then added 2 1/2 to the result, then multiplied the sum by 1 2/3 . Then I subtracted 1 2/3 and got the result 2 5/6 . What was my number?

Answer 1

Answer: The number is
`\frac3{10}` or 0.3.

Explanation:

Let x be the number.

Then,

`((x/ 1\frac12)+2\frac12)*1\frac23-1\frac23=2\frac56`

First simplify each mixed fraction into improper fraction, we get

`((x/ \frac32)+\frac52)*\frac53-\frac53=\frac{17}6\\\\\text{Now, }((x/ \frac32)+\frac52)*\frac53=(17)/(6)+\frac53\\\\\Rightarrow\ ((x/ \frac32)+\frac52)*\frac53=\frac92\\\\\Rightarrow\ ((x/ \frac32)+\frac52)=\frac92*\frac35\\\\\Rightarrow\ ((x/ \frac32)+\frac52)=(27)/(10)\\\\\Rightarrow\ (x/ \frac32)=(27)/(10)-\frac52\\\\\Rightarrow\ (x/ \frac32)=\frac2{10}\\\\\Rightarrow\ x=\frac2{10}*\frac32\\\\\Rightarrow\ x=\frac3{10}`

Hence, the number is
`\frac3{10}` or 0.3.