Question

Alex thinks of a number. He squares it, then takes away 5, next multiplies it by 4, takes away 7, devised it by 3, and finally adds 6. His answer is 9. What number did he start with ?

Answer 1

Alex's number is 3.

Explanation:

Let's call Alex's number x.

He squares it:

`x^(2)`

Then he takes away 5:

`x^(2) - 5`

Then he multiplies by 4:

`4(x^(2) - 5)`

Then takes away 7:

`4(x2 - 5) - 7`

Then he divides all that by 3:

`(4(x^(2) - 5) -7)/3`

Then he adds 6 to all that, and it equals 9:

`(4(x^(2) - 5) - 7)/3 + 6 = 9`

So let's start breaking that down. Subtract 6 from both sides to get:

`(4(x^(2) -5) - 7)/3 = 3`

Then to get rid of the one-third fraction, multiply both sides by 3:

`4(x^(2) - 5) - 7 = 9`

Add the 7 to both sides:

`4(x^(2) - 5) = 16`

Then multiply out the expression on the left:

`4x^(2) - 20 = 16`

Add 20:

`4x^(2) = 36`

Divide by 4:

`x^(2) = 9`

And then take the square root of both sides:

`x = 3`

We should test it using the words given:

• He thinks of 3.
• Squares it and gets 9.
• Takes away 5 and gets 4.
• Multiplies by 4 and gets 16.
• Takes away 7 and gets 9.
• Divides by 3 and gets 3.
• Adds 6 and gets 9.

So the answer checks out. You should always check your work by plugging the answer you found back into the given problem.