Cindy had two rolls of ribbons of the same length but different designs. She cut the first roll of ribbon into equal pieces of length 30 cm and there were 5 smileys on each piece of ribbon and cut the second roll of ribbon into equal pieces of length 40 cm and there were 8 flowers on each piece of ribbon as shown. After she finished cutting both rolls of ribbons, she counted that the total number of flowers was 92 more than the total number of smileys. 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 30 and 40.

LCM of 30 and 40 = 120

Number of sets of 30 cm in a length of 120 cm
= 120 ÷ 30
= 4

Number of sets of 40 cm in a length of 120 cm
= 120 ÷ 40
= 3

Number of smileys in a length of 120 cm
= 4 x 5
= 20

Number of flowers in a length of 120 cm
= 3 x 8
= 24

Number of more flowers than smileys in 1 set of 120 cm length
= 24 - 20
= 4

Number of sets of 4 more flowers than smileys
= 92 ÷ 4
= 23

Length of one roll of ribbon
= 23 x 120
= 2760 cm

Answer(s): 2760 cm