How to make an equation for finding four consecutive odd integers whose sum is 8?

define a variable, write an equation, and solve each problem. And then check your solution. Find four consecutive odd integers whose sum is 8.

I want to know what do they mean when they saw this. In other words, I want to know how to get the answer to this.

2 Answers
smendyka
Feb 27, 2018

See a solution process below:

Explanation:

Because these are four consecutive odd integers we can name these integers:

#n#

#n + 2#

#n + 4#

#n + 6#

Now, because these four integers sum to #8# we can write the following equation and solve for #n#:

#n + (n + 2) + (n + 4) + (n + 6) = 8#

#n + n + 2 + n + 4 + n + 6 = 8#

#n + n + n + n + 2 + 4 + 6 = 8#

#1n + 1n + 1n + 1n + 2 + 4 + 6 = 8#

#(1 + 1 + 1 + 1)n + (2 + 4 + 6) = 8#

#4n + 12 = 8#

#4n + 12 - color(red)(12) = 8 - color(red)(12)#

#4n + 0 = -4#

#4n = -4#

#(4n)/color(red)(4) = -4/color(red)(4)#

#(color(red)(cancel(color(black)(4)))n)/cancel(color(red)(4)) = -1#

#n = -1#

Therefore the 4 consecutive odd integers summing to #8# are:

#n = -1#

#n + 2 = -1 + 2 = 1#

#n + 4 = -1 + 4 = 3#

#n + 6 = -1 + 6 = 5#

#-1 + 1 + 3 + 5 = 8#

Samuel U.
Feb 27, 2018

#8 = a + b + c + d# where #a#, #b#, #c#, and #d# are all odd ?

Explanation:

I think this question requires knowledge outside of algebra to answer.

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