PSLEUsha had two strings of the same length. She cut the first string into equal parts of length 45 cm and to each part she tied 3 yellow paper cranes. After that, she cut the second string into equal parts of length 50 cm and to each part she tied 4 purple paper cranes. When she finished tying, she counted that there were 30 more purple paper cranes than yellow paper cranes. How many paper cranes were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
45 cm |
50 cm |
|
|
Number of balloons tied to each part |
3 yellow balloons |
4 purple balloons |
|
|
LCM |
450 cm |
450 cm |
|
|
Number of equal parts |
450 ÷ 45 = 10 |
450 ÷ 50 = 9 |
|
|
Number of balloons for each string per set |
10 x 3 = 30 |
4 x 9 = 36 |
36 - 30 = 6 |
30 + 36 = 66 |
LCM of 45 and 50 = 450
Number of sets of 3 yellow paper cranes in a length of 450 cm
= 450 ÷ 45
= 10
Number of yellow paper cranes in a length of 450 cm
= 10 x 3
= 30
Number of sets of 4 purple paper cranes in a length of 450 cm
= 450 ÷ 50
= 9
Number of purple paper cranes in a length of 450 cm
= 9 x 4
= 36
Extra number of purple paper cranes in a length of 450 cm
= 36 - 30
= 6
Number of sets of paper cranes
= 30 ÷ 6
= 5
Total number of paper cranes in one set of 450 cm of yellow balloons and one set of 450 cm of purple balloons
= 30 + 36
= 66
Total number of paper cranes of the two strings
= 5 x 66
= 330
Answer(s): 330