Let the smaller odd integer be: a
then the larger odd integer which is consecutive to a will be: a+2
It is given that:
Seven times the first (smaller) of two consecutive odd integers is equal to five times the second (larger) integer.
This means that:
7 times of a is equal to 5 times of (a+2)
i.e.
[tex]7a=5(a+2)\\\\i.e.\\\\7a=5\times a+5\times 2[/tex]
( Since, by using the distributive property of multiplication)
i.e.
[tex]7a=5a+10\\\\i.e.\\\\7a-5a=10\\\\i.e.\\\\2a=10\\\\i.e.\\\\a=5[/tex]
Hence, the smaller number is: 5
and the larger number is: 7
( Since a+2=5+2=7 )
