Can anyone help me on a math problem?

Question

I need to find 2 consecutive odd integers whose sum is 116, and 3 consecutive even integers whose sum is 117. I have to write an equation, and solve each problem. If you could really help me I will choose you as the best answer.:)

Answer 1

Hi Peterkarsai.

To answer your second question first, even numbers (integers) can never add up to an odd number (117).

As for the first question,

Let X equal the first integer and Y equal the second integer.

From the information given, you can write these two equations about X and Y:

1) Y = X + 2
2) X + Y = 116

Now, substitute X + 2 for Y in the second equation to yield:

X + X + 2 = 116, this equals:

2X = 114, therefore:

X = 57

Substituting 57 for X in the first equation above yields:

Y = 57 + 2, therefore:

Y = 59

Testing our results: 57 + 59 does equal 116 (and 57 and 59 are consecutive odd integers!

Answer 2

wenzhengsf does a good job with the equations but I'd check his math. For the 2 consecutive odd integers, your numbers should be more than 50 each since their sum is more 100. And you can't have 3 consecutive even integers add up to 117 since the sum of any number of even integers would also have to be even.

Answer 3

Since "wenz..etc." was wrong in his first case by a factor of ten, the answers being 57 and 59, and... in the second case was solving, again, for odd integers instead of even, as requested, may hap he can redo his math and set us all straight. However, with all due respect, even he can't get 3 even integers to add up to an odd number!!!
But then, maybe the whole thing is wrong and the 116 and 117 are in the wrong order??? Any one care to play along? Seems to me that opens up the possibility of four (4) new equations.

Answer 4

Odds:
Let the first one be 2n+1, so the second is 2n+3
They add up to 116, that is,
2n+1 + 2n+3 = 116
4n + 4 = 116
4n = 112
n = 112/4 = 28
2n+1 = 56+1 = 57
2n+3 = 56+3 = 59

Even:
2n, 2n+2, 2n+4 are the 3 consecutive evens
They add up to 117
2n + 2n+2 + 2n+4 = 6n+6 = 117
6n = 111
n = 111/6 = not an even integer

Answer 5

An odd integer can be expressed as 2n+1 where n is an integer.
The next consecutive odd integer is 2n+1+2, or 2n+3
(2n+1)+(2n+3) = 116
4n = 112
n = 28
Your integers are 2n+1 = 57
2n+3= 59

An even integer can be expressed as 2n where n is an integer.
The next consecutive even integer is 2n+2
So, 2n+(2n+2)+(2n+4) = 117
Unfortunately, you can't add even numbers to get an odd number, so you've either stated the problem wrong, or someone is pulling your leg.

Answer 6

let X be first odd number
let X+2 be second odd number
hence equation: X+X+2=116
2X=114
X=57
first odd number is 57 while second consecutive odd number is 59, X+2,57+2,59

second question:
let first even number be X
let second even number be X+2
let third even number be X+4
equation: X+X+2+X+4=117
3X=111
X=37
hence answers is 37,39,41(i think im wrong but did you say even, im not so sure abt this answer but im sure of the first one. im sorry that im of not much use)good luck with your problem sums^^

Answer 7

for sum of 2 consecutive odd # = 116
let x = odd #
x + 2 = first consecutive odd # after x
x + (x + 2) = 116
x + x + 2 = 116
2x = 114
x = 47, x + 2 = 49
the 2 consecutive #s are 47 and 49

for 3 consecutive # with sum = 117
let x = first odd #
x + 2 = first consecutive odd # after x
x + 4 = second consecutive odd # after x
x + (x + 2) + (x + 4) = 117
x + x + x + 6 = 117
3x = 111
x = 37, x + 2 = 39, x + 4 = 41
the 3 consecutive #s are 37, 39, and 41

Answer 8

the first one is x + (x+2)= 116
2x+2=116
2x=114
x= 57
x+2= 59
ur odd consecutive integers ar 57 and 59

Answer 9

57 + 59 = 116 and
37 + 39 +41 = 117
There you go my friend

Answer 10

2x - 1
plus
2(x+1) - 1
equals 116

2x plus 2(x + 1) plus 2(x + 2) equals to 117