Question #3b198

1 Answer
May 28, 2017

Answer:

#13#

Explanation:

As an alternative approach, you can start by saying that #x# is the largest number in the sequence.

In this case, the number that comes before #x# would be equal to #x -1 #.

Similarly, the number that comes before the number that comes before #x# would be

#(x-1) - 1 = x - 2#

You know that the sum of the three consecutive integers is equal to #36#, so you can say that

#(x-2) + (x-1) + x = 36#

This is equivalent to

#3x - 3 = 36#

Add #3# to both sides to get

#3x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) = 36 + 3#

#3x = 39#

Finally, divide both sides by #3#

#(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = 39/3#

to get

#color(darkgreen)(ul(color(black)(x = 13)))#