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we're told that the sum of three consecutive odd integers is 231 what is the largest integer so let's let's think about this a little bit let's say that X is the smallest integer X is equal to the smallest the smallest odd of these three it's not the smallest odd integer of all integers is the smallest odd of these three the smallest odd integer so what's the next one going to be well if I have one odd integer what's going to be the next odd integer let's think about this if X was three what's the next odd integer it's five and then what's the next one after that it's seven and the next one after that it's nine so every time when we add two so if the smallest one is X the next smallest odd integer is X plus two is equal to the next the next smallest odd integer odd I'll write integer here odd integer and then what will be the next one we're going to add two to this one right so it's going to be X plus four think about it if the smallest is three then we have X plus 2 which is 5 and then you have X plus 4 which is 7 so this will be the largest largest of the consecutive odd integer odd integer in this group and they tell us that the sum of these consecutive odd integers is 231 what is the largest integer so if I take X X plus 2 and X plus 4 and I sum them they should be equal to 231 so let's do that so we have X plus X plus 2 plus X plus 4 and this is this needs to be equal to 231 and when they ask us what's the largest one we're going to have to tell them what X plus 4 is equal to so let's just solve this equation so let's add our X terms we have 1 X 2 X 3 X's so we get 3x plus and then what our constants we have a 2 and we have a 4 so 3x plus 6 is equal to is equal to 231 now let's get rid of the 6 from the left-hand side of the equation best way to do that is to subtract 6 from both sides let's subtract 6 from both sides the left hand side we're just left with a 3x just left with the 3x the 6s cancel out the right hand side 231 minus 6 is 225 225 we get 3x is equal to 225 to isolate the X let's just divide both sides by 3 divide both sides by 3 the left hand side the 3s cancel out that was the whole point behind dividing by 3 we get just an X we get just NX is being equal to and 225 divided by 3 let me do it over here so 3 goes into 225 it goes into 22 7 times 7 times 3 is 21 22 minus 21 is 1 bring down the 5 3 goes into 15 5 times 5 times 3 is 15 subtract no remainder so 225 divided by 3 is 75 so the smallest the smallest of the odd integers is 75 so that this one is 75 what's X plus 2 going to be equal to well that's going to be 2 more 77 and what's X plus 4 going to be equal to well that's the largest of them X is 75 plus 4 is going to be 79 79 and notice we have three odd integers they're consecutive they're the you know with their the odd integers that come directly after each other and let's verify that when we add them up we get 231 so if we get 75 plus let me just write it like this 75 plus 77 + 79 want to add them all up 5 plus 7 is 12 12 plus 9 is 21 carry the 2 2 plus 7 is 9 9 plus 7 is 16 16 plus 7 is 23 so there you have it the three consecutive odd integers when you add them up you got 231 they're consecutive and odd they asked what's the largest the largest is 79