What are three consecutive integers whose sum is 51?

2 Answers
MeneerNask
Jul 3, 2018

The middle one must be the average.

Explanation:

#51div3=17#

So the numbers are #16,17,18#

Note:
This only works with an odd number of integers with constant increments. In other cases you'll have to resort to #x# equations,
in this case #x+(x+1)+(x+2)=51->x=16#

smendyka
Jul 3, 2018

See a solution process below:

Explanation:

Let's call the first integer: #n#

Then, the next two consecutive integers would be:

#n + 1# and #n + 2#

Because their sum is #51# we can write and solve the following equation for #n#:

#n + (n + 1) + (n + 2) = 51#

#n + n + 1 + n + 2 = 51#

#n + n + n + 1 + 2 = 51#

#1n + 1n + 1n + 1 + 2 = 51#

#(1 + 1 + 1)n + 1 + 2 = 51#

#3n + 3 = 51#

#3n + 3 - color(red)(3) = 51 - color(red)(3)#

#3n + 0 = 48#

#3n = 48#

#(3n)/color(red)(3) = 48/color(red)(3)#

#(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 16#

#n = 16#

Therefore:

#n + 1 = 16 + 1 = 17#

#n + 2 = 16 + 2 = 18#

The three consecutive integers which sum to 51 are 16, 17 and 18

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