Four consecutive odd integers add up to 64. What are the numbers?

1 Answer
Apr 26, 2016

#13, 15, 17 and 19#

Explanation:

Let the first odd number be #=2n+1#, where #n# is any positive integer.

Thus we have four consecutive odd numbers
#(2n+1), (2n+3), (2n+5) and (2n+7)#
Setting the sum of these numbers equal to the given value

#(2n+1)+ (2n+3)+ (2n+5) + (2n+7)=64#, simplifying
#(8n+16)=64#, dividing both sides and solving for #n#
#(n+2)=8#
or #n=8-2=6#
The numbers are
#(2xx6+1), (2xx6+3), (2xx6+5) and (2xx6+7)#
#13, 15, 17 and 19#