PSLE
Emily had two strings of the same length. She cut the first string into equal parts of length 35 cm and to each part she tied 2 white heart cutouts. After that, she cut the second string into equal parts of length 40 cm and to each part she tied 4 black heart cutouts. When she finished tying, she counted that there were 48 more black heart cutouts than white heart cutouts. How many heart cutouts were there altogether?

	First string	Second string	Difference	Total
Length of each part	35 cm	40 cm
Number of balloons tied to each part	2 white balloons	4 black balloons
LCM	280 cm	280 cm
Number of equal parts	280 ÷ 35 = 8	280 ÷ 40 = 7
Number of balloons for each string per set	8 x 2 = 16	4 x 7 = 28	28 - 16 = 12	16 + 28 = 44

LCM of 35 and 40 = 280

Number of sets of 2 white heart cutouts in a length of 280 cm
= 280 ÷ 35
= 8

Number of white heart cutouts in a length of 280 cm
= 8 x 2
= 16

Number of sets of 4 black heart cutouts in a length of 280 cm
= 280 ÷ 40
= 7

Number of black heart cutouts in a length of 280 cm
= 7 x 4
= 28

Extra number of black heart cutouts in a length of 280 cm
= 28 - 16
= 12

Number of sets of heart cutouts
= 48 ÷ 12
= 4

Total number of heart cutouts in one set of 280 cm of white balloons and one set of 280 cm of black balloons
= 16 + 28
= 44

Total number of heart cutouts of the two strings
= 4 x 44
= 176

Answer(s): 176