Question

Yaneev thinks of a number y. He subtracts three from the number, then doubles it. Then he subtracts three again, and doubles the number again. The result is his original number y. What is y?

Answer 1

Answer: y=6

Step-by-step explanation:

The given number is y.

According to the question,

Step 1 . subtracts three from the number (y-3), then doubles it

i.e. Final number = 2(y-3)

Step 2 .  subtracts three again i.e. (2(y-3)-3), and doubles the number again

i.e. Final result  = 2(2(y-3)-3)

If the result is his original number y, then

2(2(y-3)-3) =y

⇒ 2(2y-6-3)=y   [ using distributive property]

⇒ 2(2y-9)=y

⇒ 2(2y)-2(9)=y [ using distributive property]

⇒ 4y -18=y

⇒ 4y -y= 18 

⇒ 3y= 18

⇒ y= 6    [Divide both sides by 3]

Hence,  y=6