Given :
John can play 12 songs on his guitar but learns 1 new song every week. Aiden can play 4 songs but learns 2 every week.
To Find :
How many weeks will it be before Aiden knows as many songs as john?
Solution :
Let, after x weeks Aiden know a songs and John know j songs.
The linear equation for both the situation is :
a = x + 12 .....( For Aiden )
j = 2x + 4 ......( For John )
We need to find in which week Aiden knows as many songs as John.
For this , a = j
x + 12 = 2x + 4
x = 8
Therefore, in 8th week both of them know the same number of songs.