```Question 155746
hi, hope I can help,
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if the sum of three consecutive odd integers is 237 then what are the integers
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This is a pretty easy problem
First, you have to know the variables
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consecutive means "in order" (example: 1, 2, 3, ... ) here is another example: (25, 26, 27, ... )
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consecutive odd means "in order, but they have to be odd numbers" (examples: 3, 5, 7, 9, ... ) or ( 107, 109, 111, 113, ... )
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Since this is our first number, we can name it "x"
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Our second number would be "x+2" ( we have three consecutive odd integers ,meaning, if the first number is odd, you have to add 2 more to get the next odd number( example: let's say our "x" was 5, our second number would be "x+2", we replace "x" it will become "5+2" or "7", our first odd number is 5, our second is 7)
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Our third number is "x+4" (if second number is odd, have to add 2 to get the third odd number
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Your first number will always be "x"
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If you are trying to find the consecutive numbers(not consecutive odd), you add 1 for each number ( first number = "x", second = "x+1", third = "x+2", fourth = "x + 3", ...  )
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If you are finding consecutive odd( or even) numbers, you add 2 for each number
( first number always = "x") ( first number = "x", second number = "x + 2", third number = "x + 4", fourth number = "x + 6", ... )
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Since we are finding consecutive odd integers, our three numbers are( remember we start with "x" and add 2 each time)
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First number = "x"
Second number = "x + 2"
Third number = "x + 4"
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Since we know our three variables, we can know put them in a formula
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if the sum of three consecutive odd integers is 237 then what are the integers
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First number = "x"
Second number = "x + 2"
Third number = "x + 4"
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Our fomula = {{{ (x) + (x + 2) + (x + 4) = 237 }}}
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Now all we need to do is solve for "x"
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We can get rid of the parentheses, {{{ x + x + 2 + x + 4 = 237 }}}
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We will reorder the numbers, {{{ x + x + x + 4 + 2 = 237 }}}
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we will now combine like terms
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{{{ (x + x + x) + (4 + 2) = 237 }}} = {{{ 3x + 6 = 237 }}}
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we will now move "6" to the right side
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{{{ 3x + 6 - 6 = 237 - 6 }}} = {{{ 3x = 231 }}}
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We will divide each side by "3" to get "x"
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{{{ 3x/3 = 231/3 }}} = {{{ x = 231/3 }}} = {{{ x = 77 }}}
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We found that our first odd consecutive number(x) = 77
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Our second number = "x + 2" ( replace "x" with 77) = "77 + 2" = 79
Our third number = "x + 4" ( replace "x" with 77) = "77 + 4" = 81
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We can check by replacing "x" with 77 in our original equation
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{{{ (x) + (x + 2) + (x + 4) = 237 }}}
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{{{ (77) + (77 + 2) + (77 + 4) = 237 }}}
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{{{ (77) + (79) + (81) = 237 }}}
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{{{ 237 = 237 }}} ( True )
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Our three numbers are
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1st = {{{ 77 }}}
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2nd = {{{ 79 }}}
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3rd = {{{ 81 }}}
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Hope I helped, Levi```