Question

let n be the middle number of three consecutive integers. write an expression for the sum of these integers.

Answer 1

Hm...I'm trying to think of a way to give you a hint without explicitly telling you the solution. For example, 1,2, and 3 are consecutive integers. If 2 is the middle integer in this sequence, how can you express 2 in terms of the first and the third integer? :-)

Answer 2

I have no idea lol this is new to me

Answer 3

Considering the example 1,2,3 again, if 2 is the middle number, what do I do to 2 in order to get 1? What do I do to 2 in order to get 3? :-)

Answer 4

(It's easier than it looks)

Answer 5

in order to get 3 u add so it'd be like n+2 and to get 1 u would subract so 2-1

Answer 6

I think you mean 2+1. ;-)

Anyways, then it follows that we can rewrite the consecutive integers 1,2,3 in terms of the middle integer! In particular, 1,2,3 is the same as 2-1,2,2+1. Once you have this, it's very easy to generalize the result. In this case, the problem is asking for the 3 consecutive integers given that n is the second integer. Do you think you can come up with the appropriate consecutive integers now? :-)

Answer 7

is it (n-1)+n+(n+1)?

Answer 8

Yes it is. :-)

Do you know if they want you to simplify it?

Answer 9

yeah or you could just leave the problem as it is

Answer 10

Generally, I think it would be best to simplify it. What do you get in this case?

Answer 11

3n

Answer 12

Yup, that's it. :-)

Does this make a little more sense now? :-)

Answer 13

Yes it does, thanks :) can you answer another question for me?

Answer 14

Sure. :-)

Answer 15

The sum of the four angle measures of any convex quadrilateral is 360 degrees. Suppose that a convex quadrilateral has angle measures of 30 , y+10 , and 10y-8 degrees. Write an expression for the degree measure of the fourth angle.

Answer 16

Let the 4th degree measure be \(x\). Then by what you're told in the problem, we have that \(30+(y+10)+(10y-8)+x = 360\).

What do you get when you solve this equation for \(x\)? :-)

Answer 17

Do we distribute?

Answer 18

Well, we're not multiplying anything together, so there's no need to distribute. What you want to do though is combine like terms and solve for \(x\).

Answer 19

Also, because you're adding everything together, you can drop the parenthesis. I just included them to emphasize the different angles that were being added together. :-)

Answer 20

okay so is it gonna be 58+11y=360?

Answer 21

48+11y=360

Answer 22

omg im so sorry lol its 5y+10

Answer 23

30,5y+10 and 10y-8

Answer 24

so it will be 48+15y=360

Answer 25

We're trying to solve for x.

When you combine everything on the LHS, we see that \(30+y+10+10y-8 +x = x + 11y + 32\). If that's equal to 360, then \(x=360 - (11y+32) = \ldots\).

Can you take things from here?

Answer 26

I can try

Answer 27

I got 328-11y

Answer 28

Yes, that's correct! :-)

Answer 29

do we divide now or is that the answer?

Answer 30

No, that's our answer. The 4th angle measurement in terms of the 3 that were given is \(328-11y\).

Does this make more sense than it did originally? :-)

Answer 31

Yes it makes alot more sense haha

Answer 32

Chance, don't think too much!

If the middle number is n, then the first number is n-1 and the third number is n + 1.

So, we have (n - 1) + n + (n + 1). In this case, you can take out the parentheses. Combine like terms and you get 3n.

Let's check. 3 + 4 + 5 = 12 = 3(4)

5 + 6 + 7 = 18 = 3(6).

Hope this helps!