Question #1f851

1 Answer
smendyka
Feb 11, 2017

The greatest number of the three consecutive odd integers whose sum is 81 is #color(red)(29)#

Explanation:

Let's call the first of the three consecutive odd integers #x#. Then, by definition of "consecutive" and "odd" the other two numbers will be #x + 2# and #x + 4#.

The sum of these three numbers is #81# so we can write:

#x + x + 2 + x + 4 = 81#

#3x + 6 = 81#

#3x + 6 - color(red)(6) = 81 - color(red)(6)#

#3x + 0 = 75#

#3x = 75#

#(3x)/color(red)(3) = 75/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 25#

#x = 25#, this is the first integer.

The other two odd integers are:

#x + 2 = 25 + 2 = 27#

#x + 4 = 25 + 4 = 29#

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