Eleven Pipers Piping

Algebra Level 1

Eleven pipers took a break from piping. One piper said "Hey everyone give me the possible values of x in this equation:

x 2 − 12 x + 11 = 11 ( x − 1 ) { x }^{ 2 }\quad -\quad 12x\quad +\quad 11\quad =\quad 11(x\quad -\quad 1)

If you got the 2 values of x, add them together."

What is the answer to the piper's problem?


The answer is 23.

Angela Fajardo by Angela Fajardo , 19, Philippines

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1 solution

Angela Fajardo
Dec 30, 2015

x 2 − 12 x + 11 = 11 ( x − 1 ) ( x − 11 ) ( x − 1 ) = 11 ( x − 1 ) D i v i d e ( x − 1 ) t o b o t h s i d e s x − 11 = 11 ∣ x − 1 = 0 ∣ x = 22 ∣ x = 1 { x }^{ 2 }\quad -\quad 12x\quad +\quad 11\quad =\quad 11(x\quad -\quad 1)\\ \\ (x\quad -\quad 11)(x\quad -\quad 1)\quad =\quad 11(x\quad -\quad 1)\qquad Divide\quad (x\quad -\quad 1)\quad to\quad both\quad sides\\ \\ x\quad -\quad 11\quad =\quad 11\quad \quad |\qquad x\quad -\quad 1\quad =\quad 0\\ \qquad \qquad \qquad \qquad \quad |\qquad \\ x\quad =\quad 22\qquad \qquad \quad |\qquad x\quad =\quad 1

22 + 1 = 23

So, the answer is 23.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Great problem and solution,
This solution would look better which much batter LaTeX ;)

Ashish Menon - 5 years, 1 month ago

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