PSLE
Natalie had two strings of the same length. She cut the first string into equal parts of length 40 cm and to each part she tied 2 black heart cutouts. After that, she cut the second string into equal parts of length 50 cm and to each part she tied 5 red heart cutouts. When she finished tying, she counted that there were 40 more red heart cutouts than black heart cutouts. How many heart cutouts were there altogether?

	First string	Second string	Difference	Total
Length of each part	40 cm	50 cm
Number of balloons tied to each part	2 black balloons	5 red balloons
LCM	200 cm	200 cm
Number of equal parts	200 ÷ 40 = 5	200 ÷ 50 = 4
Number of balloons for each string per set	5 x 2 = 10	5 x 4 = 20	20 - 10 = 10	10 + 20 = 30

LCM of 40 and 50 = 200

Number of sets of 2 black heart cutouts in a length of 200 cm
= 200 ÷ 40
= 5

Number of black heart cutouts in a length of 200 cm
= 5 x 2
= 10

Number of sets of 5 red heart cutouts in a length of 200 cm
= 200 ÷ 50
= 4

Number of red heart cutouts in a length of 200 cm
= 4 x 5
= 20

Extra number of red heart cutouts in a length of 200 cm
= 20 - 10
= 10

Number of sets of heart cutouts
= 40 ÷ 10
= 4

Total number of heart cutouts in one set of 200 cm of black balloons and one set of 200 cm of red balloons
= 10 + 20
= 30

Total number of heart cutouts of the two strings
= 4 x 30
= 120

Answer(s): 120