solve using n as the variable:?

Question

1.find 2 consecutive integers who's sum is 79.
2.find 3 who's sum is 69.
3. find 3 consecutive intergers in which four times the sum of the first two is the same as 6 times the third.
4.find 3 consecutive intergers in whitch 3 times the sum of the first two is 16 more then the third.
5.find 3 consecutive integers in which twice the first is 57 less then three times the third.
6. find two consecutive odd integers that have a sum of 512.
7.find three consecutive integers in which the sum of the 2nd and 3rd integers is 85 more than the first.

Answer 1

n + (n + 1) = 79
2n + 1 = 79
2n = 78
n = 38
(38, 39)

n + (n + 1) + (n + 2) = 69
3n + 3 = 69
3n = 66
n = 22
(22, 23, 24)

4(n + (n+1)) = 6(n + 2)
4(2n + 1) = 6(n + 2)
8n + 4 = 6n + 12
2n = 8
n = 4
(4, 5, 6)

You should be able to do the rest based on the way I've set these up. If not, IM me.

Answer 2

I feel in a good mood. You are lucky to get this all answered. :P

1.
the the numbers be n and n+1 ( they are consequetive integers)
n+n+1=79 => 2n+1=79 => 2n=78 => n=39
the numbers are 39,40

2.
let the numbers be n-1, n, n+1
n-1+n+n+1=69 => 3n=69 => n=23
hence the numbers are 22, 23 and 24

3.
let the numbers be n-1, n, n+1
4(n-1+n)=6(n+1)
4(2n-1)=6(n+1)
8n-4=6n+6
2n=10
n=5
Hence the numbers are 4,5 and 6

4.
let the numbers be n-1, n, n+1
3(n-1+n)=n+1 +16
6n-3=n+17
5n=20
n=4
the numbers are 3,4 and 5

5.
Let the numbers be n-1, n and n+1
2(n-1)+57=3(n+1)
2n-2+57=3n+3
2n+55=3n+3
n=52
The numbers are 51, 52 and 53

6.
let the numbers be n and n+2 ( cosequetive odd integers)
n+n+2=512
2n+2=512
2n=510
n=255

The number is 255 and 257. Some people INSIST that you take 2n+1 to be and odd digit as 2n is ALWAYS even ( a multiple of 2) and if i add one it should turn odd. so 2n+1 is ALWAYS odd and 2n+3 would be the next odd integer. In the end you get the same answer no matter which way you take.

7.
let the numbers be n-1, n and n+1
(n+n+1)=n-1+85
2n+1=n+84
n=83

the numbers are 82, 83 and 84.

There you go. Good luck.

Answer 3

1. x+x+1=79
2x+1=79
2x=78
x=39
the nos r 39 n 40

2.x+x+1+x+2=69
3x=66
x=22
the nos r 22 23 24

3.4(x+x+1)=6(x+2)
8x+4=6x+12
2x=8
x=4
the nos r 4 5 6

4.3(x+x+1) =x+2 +16
6x+3=x+2+16
5x= 15
x=3
the nos r 3 4 5

5.2x +57 = 3(x+2)
2x+57= 3x+6
x=51
the nos r 51 52 53

6. x + x+2 = 512
2x+2 =512
2x=510
x=255

the nos r 255 257

7. x+1+x+2= x+85
2x+3=x+85
x=82
The nos r 82 83 84