P5 Math: Arrange the chairs in a school hall

The school attendant wanted to arrange the chairs in the school hall. If he had arranged the chairs in rows of 10, there would be 4 chairs left behind. If he had arranged the chairs in rows of 12, there would be 15 rows less than before. 

How many chairs were there in the hall?

Solution:

We can use substitution method.

The model is assuming:

• rows with 10 seats = r 
• rows with 12 seats = s

where r = s + 15

Total number of sets is constant.

10r + 4 = 12s --> 10(s + 15) + 4 = 12s --> 2s = 154 or s = 77.

Number of chair = 12 x 77 = 924.