There were some children in a concert hall. ¹₃ of the children lined up in 9 long rows and ¹₅ of the children lined up in 5 short rows. The remaining children did not line up. There are 6 more children in each short row than each long row.
(a) What fraction of the children did not line up?
(b) How many children lined up?

	Long rows	Short rows
Number	9	5
Value	1 u	1 u + 6
Total value	9 u	5 u + 30

(a)
Fraction of children who did not line up
= 1 - ¹₃  - ¹₅  
= 1 - ⁵₁₅ - ³₁₅
= 1 - ⁸₁₅
= ⁷₁₅

(b)
⁵₁₅ of the children lined up in long rows.

9 u = 5 p --- (1)

³₁₅ of the children lined up in short rows.

5 u + 30 = 3 p --- (2)

(1)_x3
27 u = 15 p --- (3)

(2)_x5
25 u + 150 = 15 p --- (4)

(3) = (4)
27 u = 25 u + 150
27 u - 25 u = 150
2 u =  150

1 u = 150 ÷ 2 = 75

Number of children who lined up
= 9 u + 5 u + 30
= 14 u + 30
= 1050 + 30
= 1080

Answer(s): (a) ⁷₁₅; (b) 1080