Question

What are the three consecutive odd integers that equal 111? After that, answer this:Are there 3 consecutive odd integers that equal 1111?

Answer 1

odd integers are 1 more than even ones
even intergers are represetned as 2n where n is a whole number
odd=2n+1
consecutive odd integers are 2 apart from each other so therefor the numbers are 2n+1,2n+1+2, 2n+1+2+2 or 2n+1, 2n+3, 2n+5
so they add up to 111
2n+1+2n+3+2n+5=111
add like terms
6n+9=111
subtract 9 from both sides
6n=102
divide both sides by 6
n=17
numbers are
2n+1,2n+3,2n+5
subsitute
2(17)+1=34+1=35
therefor since the other sare 2 more
35,37,39 are the numbers


are there 3 that equal 1111? solve and see if it is true
2n+1+2n+3+2n+5=1111
add like terms
6n+9=1111
subtract 9 from both sides
6n=1102
divide both sides by 6
n=183.666666666666
n is not whole so the answer is NO

answer are 35,37,39 and NO

Answer 2

x- the number

x
x+2
x+4
======(+)
3x+6=111
3x=105
x=35

the numbers are 35 37 39

the second problem has the same logic

x
x+2
x+4
=====(+)
3x+6=1111
3x=1105
x=368, (3) it's not an integer number

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