Question

Seven times the first (smaller) of two consecutive odd integers is equal to five times the second (larger) integer. Find each integers.

Answer 1

• The smaller consecutive odd integer is: 5

• and the larger consecutive odd integer is: 7

Explanation:

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.

`7a=5(a+2)\\\\i.e.\\\\7a=5* a+5* 2`

( Since, by using the distributive property of multiplication)

i.e.

`7a=5a+10\\\\i.e.\\\\7a-5a=10\\\\i.e.\\\\2a=10\\\\i.e.\\\\a=5`

Hence, the smaller number is: 5

and the larger number is: 7

( Since a+2=5+2=7 )