Three consecutive odd numbers have a sum of 75. What is the greatest number?
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"What does Hess's law say about the enthalpy of a reaction?"
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
The largest or greatest number is 27.
The other two numbers are 23 and 25.
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#
