PSLECindy had two streamers of the same length. She cut the first streamer into equal parts of length 15 cm and to each part she tied 2 purple flags. After that, she cut the second streamer into equal parts of length 20 cm and to each part she tied 5 pink flags. When she finished tying, she counted that there were 14 more pink flags than purple flags. How many flags were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
15 cm |
20 cm |
|
|
Number of balloons tied to each part |
2 purple balloons |
5 pink balloons |
|
|
LCM |
60 cm |
60 cm |
|
|
Number of equal parts |
60 ÷ 15 = 4 |
60 ÷ 20 = 3 |
|
|
Number of balloons for each streamer per set |
4 x 2 = 8 |
5 x 3 = 15 |
15 - 8 = 7 |
8 + 15 = 23 |
LCM of 15 and 20 = 60
Number of sets of 2 purple flags in a length of 60 cm
= 60 ÷ 15
= 4
Number of purple flags in a length of 60 cm
= 4 x 2
= 8
Number of sets of 5 pink flags in a length of 60 cm
= 60 ÷ 20
= 3
Number of pink flags in a length of 60 cm
= 3 x 5
= 15
Extra number of pink flags in a length of 60 cm
= 15 - 8
= 7
Number of sets of flags
= 14 ÷ 7
= 2
Total number of flags in one set of 60 cm of purple balloons and one set of 60 cm of pink balloons
= 8 + 15
= 23
Total number of flags of the two streamers
= 2 x 23
= 46
Answer(s): 46