SOLUTION: I'm thinking of an integer. half of this integer is 3 more then one third of the next integer. What is the integer? Please help, I've tried everyway I can think of but none of t

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Question 255696: I'm thinking of an integer. half of this integer is 3 more then one third of the next integer. What is the integer?
Please help, I've tried everyway I can think of but none of them work,
Thank you.
Found 2 solutions by Theo, CharlesG2:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = an integer
x + 1 = the next integer

your equation to solve is:

x%2F2+=+%28x%2B1%29%2F3+%2B+3

multiply both sides of this equation by 2 to get:

x+=+2+%2A+%28+%28x%2B1%29%2F3+%2B+3%29

simplify by multiplying out the factors to get:

x+=+%282+%2A+%28x%2B1%29%29%2F3+%2B+2%2A3

simplify further to get:

x+=+%282%2Ax+%2B+2%29%2F3+%2B+6

multiply both sides of this equation by 3 to get:

3%2Ax+=+2%2Ax+%2B+2+%2B+18

subtract 2*x from both sides of the equation to get:

3%2Ax+-+2%2Ax+=+2+%2B+18

combine like terms to get:

x+=+20

since x = 20, then the next integer is x+1 = 21

your integers are 20 and 21

take half of 20 to get 10

take 21 and divide it by 3 to get 7 and then add 3 to that to get 10.

half of 20 = 10 and one third of 21 + 3 = 10, so they are equal to each other.

you get:

half of 20 = 3 more than 1/3 of 21.

your answer is that the integer is equal to 20.

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
I'm thinking of an integer. half of this integer is 3 more then one third of the next integer. What is the integer?
Please help, I've tried everyway I can think of but none of them work,
Thank you.
integer I
integer J is next integer after I
1/2 I = 1/3 J + 3
I = 2/3 J + 6
3 I = 2 J + 18
3I - 18 = 2 J
(3/2) I - 9 = J
I=(2/3)(I+1)+6
I=(2/3)I+(2/3)+6 --> 6 is 18/3
I=(2/3)I+(20/3)
3I=2I+20
I=20
lets see if 20 works for I
(1/2)(20)=(1/3)J+3
10=(1/3)J+3
7=(1/3)J
21=J
since J is next integer J must be I+1
1/2 I suggests I must be even (so result would be an integer as well)
20 is even
1/3 J suggests J must be odd and divisible by 3 (since J is next integer and so result would be integer as well)
21 is odd and divisble by 3
and 2/3 J must be an integer so I would still be an integer
14 is an integer
and 3/2 I must be an integer so J would still be an integer
30 is an integer