There were some children in a theme park. ¹₃ of the children lined up in 8 short rows and ¹₅ of the children lined up in 4 long rows. The remaining children did not line up. There are 11 more children in each long row than each short row.
(a) What fraction of the children did not line up?
(b) How many children lined up?

	Short rows	Long rows
Number	8	4
Value	1 u	1 u + 11
Total value	8 u	4 u + 44

(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 short rows.

8 u = 5 p --- (1)

³₁₅ of the children lined up in long rows.

4 u + 44 = 3 p --- (2)

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

(2)_x5
20 u + 220 = 15 p --- (4)

(3) = (4)
24 u = 20 u + 220
24 u - 20 u = 220
4 u =  220

1 u = 220 ÷ 4 = 55

Number of children who lined up
= 8 u + 4 u + 44
= 12 u + 44
= 660 + 44
= 704

Answer(s): (a) ⁷₁₅; (b) 704