PSLEDiana had two streamers of the same length. She cut the first streamer into equal parts of length 50 cm and to each part she tied 2 gold flags. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 5 purple flags. When she finished tying, she counted that there were 27 more purple flags than gold flags. How many flags were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
50 cm |
80 cm |
|
|
Number of balloons tied to each part |
2 gold balloons |
5 purple balloons |
|
|
LCM |
400 cm |
400 cm |
|
|
Number of equal parts |
400 ÷ 50 = 8 |
400 ÷ 80 = 5 |
|
|
Number of balloons for each streamer per set |
8 x 2 = 16 |
5 x 5 = 25 |
25 - 16 = 9 |
16 + 25 = 41 |
LCM of 50 and 80 = 400
Number of sets of 2 gold flags in a length of 400 cm
= 400 ÷ 50
= 8
Number of gold flags in a length of 400 cm
= 8 x 2
= 16
Number of sets of 5 purple flags in a length of 400 cm
= 400 ÷ 80
= 5
Number of purple flags in a length of 400 cm
= 5 x 5
= 25
Extra number of purple flags in a length of 400 cm
= 25 - 16
= 9
Number of sets of flags
= 27 ÷ 9
= 3
Total number of flags in one set of 400 cm of gold balloons and one set of 400 cm of purple balloons
= 16 + 25
= 41
Total number of flags of the two streamers
= 3 x 41
= 123
Answer(s): 123