What are serial numbers and consecutive numbers

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Linear equations - word problems

Video transcript

The sum of four consecutive odd integers is 136. Which four are the integers? Before we get down to the solution, we should consider what a continuous odd integer is, what four odd consecutive integers might refer to. At the beginning we could have a three. We want consecutive odd numbers. The next odd number would be five. The number after that would be seven and the next nine. These are consecutive odd integers. Another example - we could start at eleven. The next odd integer is 13. The next is 15. The next is 17. As an example of non-consecutive odd integers, if someone jumps from three straight to seven, they are not consecutive. The next odd integer after three is five, not seven. These are examples of consecutive odd integers. These are not consecutive odd integers. After that is cleared up, we can resolve this question. I encourage you to pause this video now and try the solution for yourself before trying. As you can imagine, a little algebra is useful here. Let X be equal to the smallest of the four numbers. If x is the smallest of the four consecutive odd numbers, how can we express the other three in terms of x? We use these examples here. If this is x, then how would we express that in terms of x? That would be x plus two. The next odd integer will be the previous number plus two. Basically, you're skipping the next number that will be even. If you were to add one, the number would be even, so you need to add two to get the next odd. If you add two more, if you add two to x plus two, you get x plus four. You add two to that. You get x plus six. Here you see it again. If this were x, then that is x plus two. This is x plus four and this is x plus six. In general, if x is the smallest of the numbers, we can define the other three as x plus two, x plus four, and x plus six. Let's look at their sum and define it as equal to 136 and then solve it for x. So the smallest is x. The next one will be x plus two. The next one will be x plus four, and the next one will be x plus six. This is the sum of the four consecutive odd numbers, and these tell us that this will be equal to 136. This equals 136. Now we can solve for x. We have this stranger here. Let's add these x expressions together. We have one x, two x, three x, four x. We can rewrite them to 4x. Then we have two plus four, which is six, plus another six, so twelve. 4x plus twelve equals 136. To solve x, a good start would be to isolate the x terms on either side of the equation, or to try to get rid of those twelve. To get rid of those twelve we need to subtract twelve from the left. But not just on the left. Then this equation would no longer be valid. If both sides are the same before we subtract twelve, if we want them to remain the same, if we want both sides to remain the same, then we have to subtract twelve from both sides. If we subtract twelve from both sides, we only have 4x left on the left side. On the right hand side we get 136 minus twelve, that's 124. Right? Yes, 124. What is x? We divide both sides by four to get x. And we get: x is equal to 124 divided by four. Let's see. 100 divided by four is 25. 24 divided by four is six. 25 plus six is ​​31. If you don't want to solve this in your head, you can also do a written division. One cannot be divided by four. Four fits three times in twelve. Three times four is twelve. You subtract, pull down the next four. Four fits once in four. There is no residue left. X is equal to 31. X is the smallest of the four integers. So this x here is 31. X plus two is 33. X plus four is 35. And x plus six is ​​37. So our four consecutive odd integers are 31, 33, 35, and 37.