PSLEShiyun had two strings of the same length. She cut the first string into equal parts of length 30 cm and to each part she tied 2 black paper cranes. After that, she cut the second string into equal parts of length 35 cm and to each part she tied 5 brown paper cranes. When she finished tying, she counted that there were 80 more brown paper cranes than black paper cranes. How many paper cranes were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
30 cm |
35 cm |
|
|
Number of balloons tied to each part |
2 black balloons |
5 brown balloons |
|
|
LCM |
210 cm |
210 cm |
|
|
Number of equal parts |
210 ÷ 30 = 7 |
210 ÷ 35 = 6 |
|
|
Number of balloons for each string per set |
7 x 2 = 14 |
5 x 6 = 30 |
30 - 14 = 16 |
14 + 30 = 44 |
LCM of 30 and 35 = 210
Number of sets of 2 black paper cranes in a length of 210 cm
= 210 ÷ 30
= 7
Number of black paper cranes in a length of 210 cm
= 7 x 2
= 14
Number of sets of 5 brown paper cranes in a length of 210 cm
= 210 ÷ 35
= 6
Number of brown paper cranes in a length of 210 cm
= 6 x 5
= 30
Extra number of brown paper cranes in a length of 210 cm
= 30 - 14
= 16
Number of sets of paper cranes
= 80 ÷ 16
= 5
Total number of paper cranes in one set of 210 cm of black balloons and one set of 210 cm of brown balloons
= 14 + 30
= 44
Total number of paper cranes of the two strings
= 5 x 44
= 220
Answer(s): 220