Three consecutive odd numbers have a sum of 75. What is the greatest number?

2 Answers
Nov 27, 2016

26

Explanation:

Let the three consecutive nos are #(x-1)#, #(x)# & #(x+1)#.

As per question,

#(x-1) + (x) + (x+1)# = 75

#3x# = 75

#x = 75/3 = 25#

Therefore the largest no = #x+1# = 25 + 1 = 26

Nov 27, 2016

The largest or greatest number is 27.

The other two numbers are 23 and 25.

Explanation:

Let's call the largest odd number #x# because this is what we are solving for.

If #x# is the largest odd number and these are consecutive odd numbers we must subtract #2# and #4# from #x# to get all three consecutive odd numbers.

So, the three consecutive odd numbers are: #x - 4#, #x - 2# and #x#.

We know their sum, or adding them together, is #75# so we can write and solve for #x#:

#(x - 4) + (x - 2) + x = 75#

#x - 4 + x - 2 + x = 75#

#x + x + x - 4 - 2 = 75#

#3x - 6 = 75#

#3x - 6 + 6 = 75 + 6#

#3x = 81#

(3x)/3 = 81/3#

#x = 27#