PSLEShannon had two streamers of the same length. She cut the first streamer into equal parts of length 30 cm and to each part she tied 2 grey flags. After that, she cut the second streamer into equal parts of length 40 cm and to each part she tied 5 black flags. When she finished tying, she counted that there were 35 more black flags than grey flags. How many flags were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
30 cm |
40 cm |
|
|
Number of balloons tied to each part |
2 grey balloons |
5 black balloons |
|
|
LCM |
120 cm |
120 cm |
|
|
Number of equal parts |
120 ÷ 30 = 4 |
120 ÷ 40 = 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 30 and 40 = 120
Number of sets of 2 grey flags in a length of 120 cm
= 120 ÷ 30
= 4
Number of grey flags in a length of 120 cm
= 4 x 2
= 8
Number of sets of 5 black flags in a length of 120 cm
= 120 ÷ 40
= 3
Number of black flags in a length of 120 cm
= 3 x 5
= 15
Extra number of black flags in a length of 120 cm
= 15 - 8
= 7
Number of sets of flags
= 35 ÷ 7
= 5
Total number of flags in one set of 120 cm of grey balloons and one set of 120 cm of black balloons
= 8 + 15
= 23
Total number of flags of the two streamers
= 5 x 23
= 115
Answer(s): 115