Pick a number. Double it. Multiply the result by 3, then add 24. Divide the new result by 6, and then subtract the original number. Is the result always the same? Explain why or why not.

Question

anonymous · Answer

I have tested this out using 3 different numbers, 7, 10 and 105 and HAVE gotten the same result each time. 4. but why is it the same result every time? that is the part i do not understand

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

"Pick a number"

let's make x the unknown number

jim_thompson5910 · Answer

"Double it."

so x turns into 2x

2x is the same as 2*x or 2 times x

jim_thompson5910 · Answer

"Multiply the result by 3"

we take 2x and multiply by 3

3*2x = 6x

jim_thompson5910 · Answer

"then add 24"

so we now have 6x+24

jim_thompson5910 · Answer

"Divide the new result by 6" 

$$\Large \frac{6x+24}{6} = \frac{6x}{6} + \frac{24}{6} = x + 4$$

so that gives us x+4. Now "subtract the original number"

take "x+4" and subtract off x

(x+4) - ( x ) = x + 4 - x = 4 + x - x = 4 + 0x = 4 + 0 = 4

jim_thompson5910 · Answer

so no matter what number you originally pick for x, you'll always get the same result back (4)

anonymous · Answer

so is that because subtracting the number at the end cancels out the fact that we doubled the x number at the beginning?

jim_thompson5910 · Answer

well all the steps work together in a way. It's not just that one step