There were some children in a safari park. ¹₄ of the children lined up in 10 long rows and ¹₆ of the children lined up in 6 short rows. The remaining children did not line up. There are 7 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	10	6
Value	1 u	1 u + 7
Total value	10 u	6 u + 42

(a)
Fraction of children who did not line up
= 1 - ¹₄  - ¹₆  
= 1 - ³₁₂ - ²₁₂
= 1 - ⁵₁₂
= ⁷₁₂

(b)
³₁₂ of the children lined up in long rows.

10 u = 3 p --- (1)

²₁₂ of the children lined up in short rows.

6 u + 42 = 2 p --- (2)

(1)_x2
20 u = 6 p --- (3)

(2)_x3
18 u + 126 = 6 p --- (4)

(3) = (4)
20 u = 18 u + 126
20 u - 18 u = 126
2 u =  126

1 u = 126 ÷ 2 = 63

Number of children who lined up
= 10 u + 6 u + 42
= 16 u + 42
= 1008 + 42
= 1050

Answer(s): (a) ⁷₁₂; (b) 1050