Tina had two rolls of ribbons of the same length but different designs. She cut the first roll of ribbon into equal pieces of length 20 cm and there were 7 hearts on each piece of ribbon and cut the second roll of ribbon into equal pieces of length 30 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 90 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 20 and 30.

LCM of 20 and 30 = 60

Number of sets of 20 cm in a length of 60 cm
= 60 ÷ 20
= 3

Number of sets of 30 cm in a length of 60 cm
= 60 ÷ 30
= 2

Number of hearts in a length of 60 cm
= 3 x 7
= 21

Number of stars in a length of 60 cm
= 2 x 9
= 18

Number of more hearts than stars in 1 set of 60 cm length
= 21 - 18
= 3

Number of sets of 3 more hearts than stars
= 90 ÷ 3
= 30

Length of one roll of ribbon
= 30 x 60
= 1800 cm

Answer(s): 1800 cm