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 pink paper cranes. After that, she cut the second streamer into equal parts of length 40 cm and to each part she tied 4 yellow paper cranes. When she finished tying, she counted that there were 20 more yellow paper cranes than pink 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 pink balloons |
4 yellow 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 |
4 x 5 = 20 |
20 - 16 = 4 |
16 + 20 = 36 |
LCM of 25 and 40 = 200
Number of sets of 2 pink paper cranes in a length of 200 cm
= 200 ÷ 25
= 8
Number of pink paper cranes in a length of 200 cm
= 8 x 2
= 16
Number of sets of 4 yellow paper cranes in a length of 200 cm
= 200 ÷ 40
= 5
Number of yellow paper cranes in a length of 200 cm
= 5 x 4
= 20
Extra number of yellow paper cranes in a length of 200 cm
= 20 - 16
= 4
Number of sets of paper cranes
= 20 ÷ 4
= 5
Total number of paper cranes in one set of 200 cm of pink balloons and one set of 200 cm of yellow balloons
= 16 + 20
= 36
Total number of paper cranes of the two streamers
= 5 x 36
= 180
Answer(s): 180