here are some fun question to do but the hard part is to show work.?

Question

1. the sum of two consecutive integers is 28.find the integer.
2.the sum fo an integer and 15 more than the integer is 57. Find the integer.
3.The sum of three consecutive integers is -30.what are the integers?
4.The sides of a triangle are consecutive integers. If the perimeter of the triangle is 240 unites, find the length of each side

Answer 1

1. Two consecutive integers cannot sum to give you an even number. (You might have the problem wrong)

2. n + (n+15) = 57
2n + 15 = 57
2n = 42
n = 42/2
n = 21


3. n + (n+1) + (n+2) = -30
3n + 3 = -30
3n = -33
n = -33 / 3
n = -11
So the integers are (-11, -10, -9}

4. n + (n+1) + (n+2) = 240
3n + 3 = 240
3n = 237
n = 237 / 3
n = 79
So the sides are {79, 80, 81}

Answer 2

1. The first problem is impossible to solve, because the sum of any two consecutive integers is odd and 28 is even.
2. 21 and 36; x + x + 15 = 57 and 2x = 42, so x = 21 and x + 15 = 36.
3. -9, -10, and -11:

x + x + 1 + x + 2 = -30
3x + 3 = -30
3x = -33
x = -11
x + 1 = -10
x + 2 = -9

4. 79, 80, and 81 units each; substitute 240 for -30 in the above equation and solve.

Answer 3

1. There is no such pair of integers. The sum of two consecutive integers will always be an odd number.
2.
x + x + 15 = 57
2x = 42
x = 21
x + 15 = 36
3.
- 30/3 = - 10
- 11 - 10 - 9 = - 30
4. 240/3 = 80
79 + 80 + 81 = 240

Answer 4

1) You know the sum is 28, so let's assign each integer a variable: x and y.
x+y=28
Then because they are consecutive, their difference is 1 [like 5,6 or 99, 100, any consecutive integers will have a difference of 1], so your other function (assuming y is the larger number) is
y-x=1

using elimination, you can solve for y. if you re-write the second equation as -x+y, you'll see that you have opposite signs for x in each equation
So solving using elimination you have:
x+y=28
-x+y=1
-----------
2y=29
>> y=14.5


x+14.5=28
>> x=13.5

2) x+15=y
x+y=57



x+x+15=57
2x+15=57
2x=42
x=21

3) x+y+z= -30

*remember #1? the next two equations are similar. because they are conssecutive, their difference is 1*

z-y=1
y-x=1

Now use elimination
x+y+z= -30
-y+z= 1
----------------
* x +2z= -29

-y+z=1
y -x= 1
----------
* -x+z=2

Now use those two equations we found and reduce THEM

>>> x+2z= -29
-x+ z= 2
------------------
3z= -27

Now solve for z and plug it back in and find the other variables.

4) exactly the same way as #3 I'm not going over another one!!!

I hope this helps sorry my answer is so long. You better not be gettin any more homework answers from Yahoo now okay? you should understand how to do it yourself now!

Answer 5

1. x + x + 1 = 28

2x = 27 since x is not an integer it cannot be done. Any 2 consecutine integers, 1 even, the other odd, will always add to be an odd number.



2. x + x + 15 = 57
2x = 42
x=21


3. x + x+1 + x + 2 = -30
3x + 3 = -30
3x = -33
x= -11


-11,-10.-9


4. x + x + 1 + x + 2 = 240
3x + 3 = 240
3x = 237
x=79

79,80,81