PSLEGillian had two streamers of the same length. She cut the first streamer into equal parts of length 70 cm and to each part she tied 2 blue stars. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 5 white stars. When she finished tying, she counted that there were 38 more white stars than blue stars. How many stars were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
70 cm |
80 cm |
|
|
Number of balloons tied to each part |
2 blue balloons |
5 white balloons |
|
|
LCM |
560 cm |
560 cm |
|
|
Number of equal parts |
560 ÷ 70 = 8 |
560 ÷ 80 = 7 |
|
|
Number of balloons for each streamer per set |
8 x 2 = 16 |
5 x 7 = 35 |
35 - 16 = 19 |
16 + 35 = 51 |
LCM of 70 and 80 = 560
Number of sets of 2 blue stars in a length of 560 cm
= 560 ÷ 70
= 8
Number of blue stars in a length of 560 cm
= 8 x 2
= 16
Number of sets of 5 white stars in a length of 560 cm
= 560 ÷ 80
= 7
Number of white stars in a length of 560 cm
= 7 x 5
= 35
Extra number of white stars in a length of 560 cm
= 35 - 16
= 19
Number of sets of stars
= 38 ÷ 19
= 2
Total number of stars in one set of 560 cm of blue balloons and one set of 560 cm of white balloons
= 16 + 35
= 51
Total number of stars of the two streamers
= 2 x 51
= 102
Answer(s): 102