PSLENatalie 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 4 grey paper cranes. After that, she cut the second string into equal parts of length 35 cm and to each part she tied 5 red paper cranes. When she finished tying, she counted that there were 4 more red paper cranes than grey 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 |
4 grey balloons |
5 red 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 4 = 28 |
5 x 6 = 30 |
30 - 28 = 2 |
28 + 30 = 58 |
LCM of 30 and 35 = 210
Number of sets of 4 grey paper cranes in a length of 210 cm
= 210 ÷ 30
= 7
Number of grey paper cranes in a length of 210 cm
= 7 x 4
= 28
Number of sets of 5 red paper cranes in a length of 210 cm
= 210 ÷ 35
= 6
Number of red paper cranes in a length of 210 cm
= 6 x 5
= 30
Extra number of red paper cranes in a length of 210 cm
= 30 - 28
= 2
Number of sets of paper cranes
= 4 ÷ 2
= 2
Total number of paper cranes in one set of 210 cm of grey balloons and one set of 210 cm of red balloons
= 28 + 30
= 58
Total number of paper cranes of the two strings
= 2 x 58
= 116
Answer(s): 116