PSLEDiana had two streamers of the same length. She cut the first streamer into equal parts of length 25 cm and to each part she tied 2 brown paper cranes. After that, she cut the second streamer into equal parts of length 40 cm and to each part she tied 5 red paper cranes. When she finished tying, she counted that there were 18 more red paper cranes than brown paper cranes. How many paper cranes were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
25 cm |
40 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
5 red balloons |
|
|
LCM |
200 cm |
200 cm |
|
|
Number of equal parts |
200 ÷ 25 = 8 |
200 ÷ 40 = 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 25 and 40 = 200
Number of sets of 2 brown paper cranes in a length of 200 cm
= 200 ÷ 25
= 8
Number of brown paper cranes in a length of 200 cm
= 8 x 2
= 16
Number of sets of 5 red paper cranes in a length of 200 cm
= 200 ÷ 40
= 5
Number of red paper cranes in a length of 200 cm
= 5 x 5
= 25
Extra number of red paper cranes in a length of 200 cm
= 25 - 16
= 9
Number of sets of paper cranes
= 18 ÷ 9
= 2
Total number of paper cranes in one set of 200 cm of brown balloons and one set of 200 cm of red balloons
= 16 + 25
= 41
Total number of paper cranes of the two streamers
= 2 x 41
= 82
Answer(s): 82