PSLEUsha had two streamers of the same length. She cut the first streamer into equal parts of length 60 cm and to each part she tied 3 blue stars. After that, she cut the second streamer into equal parts of length 70 cm and to each part she tied 5 red stars. When she finished tying, she counted that there were 45 more red stars than blue stars. How many stars were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
60 cm |
70 cm |
|
|
Number of balloons tied to each part |
3 blue balloons |
5 red balloons |
|
|
LCM |
420 cm |
420 cm |
|
|
Number of equal parts |
420 ÷ 60 = 7 |
420 ÷ 70 = 6 |
|
|
Number of balloons for each streamer per set |
7 x 3 = 21 |
5 x 6 = 30 |
30 - 21 = 9 |
21 + 30 = 51 |
LCM of 60 and 70 = 420
Number of sets of 3 blue stars in a length of 420 cm
= 420 ÷ 60
= 7
Number of blue stars in a length of 420 cm
= 7 x 3
= 21
Number of sets of 5 red stars in a length of 420 cm
= 420 ÷ 70
= 6
Number of red stars in a length of 420 cm
= 6 x 5
= 30
Extra number of red stars in a length of 420 cm
= 30 - 21
= 9
Number of sets of stars
= 45 ÷ 9
= 5
Total number of stars in one set of 420 cm of blue balloons and one set of 420 cm of red balloons
= 21 + 30
= 51
Total number of stars of the two streamers
= 5 x 51
= 255
Answer(s): 255