What are three consecutive integers so that the sum of the second and third is sixteen more than the first?

1 Answer
Ricardo A.
Oct 2, 2016

13,14 and 15

Explanation:

So we want 3 integers that are consecutive (such as 1, 2, 3). We don't know them (yet) but we'd write them as x, x+1 and x+2.

Now the second condition of our problem is that the sum of the second and third numbers (x+1 and x+2) must equal the first plus 16 (x+16). We would write that like this:

#(x+1)+(x+2)=x+16#
Now we solve that equation for x:
#x+1+x+2=x+16#
add 1 and 2
#x+x+3=x+16#
subtract x from both sides:
#x+x-x+3=x-x+16#
#x+3=16#
subtract 3 from both sides:
#x+3-3=16-3#
#x=13#
So the numbers are:
#x=13#
#x+1=14#
#x+2=15#

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