Fanny had two rolls of ribbons of the same length but different designs. She cut the first roll of ribbon into equal pieces of length 36 cm and there were 7 hearts on each piece of ribbon and cut the second roll of ribbon into equal pieces of length 54 cm and there were 9 stars on each piece of ribbon as shown. After she finished cutting both rolls of ribbons, she counted that the total number of hearts was 54 more than the total number of stars. Find the length of one roll of ribbon in cm.
To make the lengths of the two rolls of ribbons were the same, find the LCM of 36 and 54.

LCM of 36 and 54 = 108

Number of sets of 36 cm in a length of 108 cm
= 108 ÷ 36
= 3

Number of sets of 54 cm in a length of 108 cm
= 108 ÷ 54
= 2

Number of hearts in a length of 108 cm
= 3 x 7
= 21

Number of stars in a length of 108 cm
= 2 x 9
= 18

Number of more hearts than stars in 1 set of 108 cm length
= 21 - 18
= 3

Number of sets of 3 more hearts than stars
= 54 ÷ 3
= 18

Length of one roll of ribbon
= 18 x 108
= 1944 cm

Answer(s): 1944 cm