(5x - 7) + (10x 7) = 180
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We are told that the children from a football club are put into rows in the sports hall. When put into rows of 9 children there are 2 children left over. When put into rows of 12 children there are 2 children left over.
We will find least number of children in football club by finding LCM of 9 and 12.
Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63,...
Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,...
We can see that least common multiple of 9 and 12 is 36.
We are told that 2 children left over from putting them into 9 and 12 children per row. To find least number we will add 2 to 36.
Therefore, the least number of children in the football club is 38.