There were some children in a museum. ¹₄ of the children lined up in 10 short rows and ¹₃ of the children lined up in 6 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	10	6
Value	1 u	1 u + 11
Total value	10 u	6 u + 66

(a)
Fraction of children who did not line up
= 1 - ¹₄  - ¹₃  
= 1 - ³₁₂ - ⁴₁₂
= 1 - ⁷₁₂
= ⁵₁₂

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

10 u = 3 p --- (1)

⁴₁₂ of the children lined up in long rows.

6 u + 66 = 4 p --- (2)

(1)_x4
40 u = 12 p --- (3)

(2)_x3
18 u + 198 = 12 p --- (4)

(3) = (4)
40 u = 18 u + 198
40 u - 18 u = 198
22 u =  198

1 u = 198 ÷ 22 = 9

Number of children who lined up
= 10 u + 6 u + 66
= 16 u + 66
= 144 + 66
= 210

Answer(s): (a) ⁵₁₂; (b) 210