[Math] Integer word problem?

Question

I'm currently stuck on a set of problems that the book doesn't have examples for, e.g:

"Nine times the first of two consecutive odd integers equals seven times the second. Find the integers."

Answer 1

Let 2x+1 be the first odd integer
Then 2x+3 = the next consecutive odd integer
So 9(2x+1) = 7(2x+3)
18x+9 = 14x+21
4x = 12
x = 3
2x+1 = 7 = the 1st odd integer
2x+3 = 9 = the 2nd odd integer

Answer 2

Two consecutive odd integers: x and x +2

9 x = 7 (x+2)
9 x = 7 x +14
x = 7

Therefore, your two numbers are 7 and 9.

:)

Answer 3

Let the first Odd integer be X
Then the next odd integer will be=x+2
Therefore 9(X)=7(x+2)
Or 9x-7x=14
Or 2x=14
Or x=7
Therefore no's are 7&9

Answer 4

Let N be the first odd integer, and N+2 be the next consecutive odd integer.

9N = 7(N+2)
9N = 7N + 14
2N = 14
N = 7
N+2 = 9

Answer 5

Let consecutive odd numbers be x & x+2
Then, 9(x) = 7(x+2)
Whence, x = 7 since 9*7=7*9.

Answer 6

let the two consecutive odd integers be (2n+1)and (2n+3):
9(2n+1)=7(2n+3)
4n=12
n=3
so the two cosecutive odd integers are 7&9
verified. OK.

Answer 7

9x = 7(x+2) :consecutive odd integers are spaced in two's.

9x = 7x+ 14

2x = 14
x = 7

so the integers are 7 and 9

Answer 8

translation of your problem is :

x=2k+1
y=2k+3
(with k and integer)
9*x= 7*y

find x and y.


can be solved easily by subsitution.
9*(2k+1) = 7*(2k+3)
18k+9 = 14k+21
therefore (18-14)k = 21-9
k=12/4 = 3

x = 2k+1 = 7
y = 9

Answer 9

n=m+2
9m=7n

9m=7(m+2)
9m=7m+14
2m=14
m=7
n=9