PSLE
Penelope had two strings of the same length. She cut the first string into equal parts of length 30 cm and to each part she tied 3 black paper cranes. After that, she cut the second string into equal parts of length 40 cm and to each part she tied 5 purple paper cranes. When she finished tying, she counted that there were 9 more purple paper cranes than black paper cranes. How many paper cranes were there altogether?

	First string	Second string	Difference	Total
Length of each part	30 cm	40 cm
Number of balloons tied to each part	3 black balloons	5 purple balloons
LCM	120 cm	120 cm
Number of equal parts	120 ÷ 30 = 4	120 ÷ 40 = 3
Number of balloons for each string per set	4 x 3 = 12	5 x 3 = 15	15 - 12 = 3	12 + 15 = 27

LCM of 30 and 40 = 120

Number of sets of 3 black paper cranes in a length of 120 cm
= 120 ÷ 30
= 4

Number of black paper cranes in a length of 120 cm
= 4 x 3
= 12

Number of sets of 5 purple paper cranes in a length of 120 cm
= 120 ÷ 40
= 3

Number of purple paper cranes in a length of 120 cm
= 3 x 5
= 15

Extra number of purple paper cranes in a length of 120 cm
= 15 - 12
= 3

Number of sets of paper cranes
= 9 ÷ 3
= 3

Total number of paper cranes in one set of 120 cm of black balloons and one set of 120 cm of purple balloons
= 12 + 15
= 27

Total number of paper cranes of the two strings
= 3 x 27
= 81

Answer(s): 81