Algebra is Fun

Number Theory Level 2

What is the smallest value of x + y x+y given that 2013 x = 12 y 2013x = 12y and x x and y y are positive integers?


The answer is 675.

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Christian Daang by Christian Daang , 20, Philippines

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2 solutions

Mona Lisha
Nov 3, 2014

2013x=12y cross multiply 2013/12=y/x=671/4 so y=671 and x=4 as x and y are integers so,x+y=675

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Christian Daang
Oct 26, 2014

base from the given, 2013x = 12y

----> 671x = 4y

we can clearly see that.. The minimum value of x = 4 and y = 671..

Therefore, x+y = 4+671 = 675.

Final Answer. 675.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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