PSLENatalie had two ribbons of the same length. She cut the first ribbon into equal parts of length 80 cm and to each part she tied 4 purple paper cranes. After that, she cut the second ribbon into equal parts of length 90 cm and to each part she tied 5 black paper cranes. When she finished tying, she counted that there were 20 more black paper cranes than purple paper cranes. How many paper cranes were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
80 cm |
90 cm |
|
|
Number of balloons tied to each part |
4 purple balloons |
5 black balloons |
|
|
LCM |
720 cm |
720 cm |
|
|
Number of equal parts |
720 ÷ 80 = 9 |
720 ÷ 90 = 8 |
|
|
Number of balloons for each ribbon per set |
9 x 4 = 36 |
5 x 8 = 40 |
40 - 36 = 4 |
36 + 40 = 76 |
LCM of 80 and 90 = 720
Number of sets of 4 purple paper cranes in a length of 720 cm
= 720 ÷ 80
= 9
Number of purple paper cranes in a length of 720 cm
= 9 x 4
= 36
Number of sets of 5 black paper cranes in a length of 720 cm
= 720 ÷ 90
= 8
Number of black paper cranes in a length of 720 cm
= 8 x 5
= 40
Extra number of black paper cranes in a length of 720 cm
= 40 - 36
= 4
Number of sets of paper cranes
= 20 ÷ 4
= 5
Total number of paper cranes in one set of 720 cm of purple balloons and one set of 720 cm of black balloons
= 36 + 40
= 76
Total number of paper cranes of the two ribbons
= 5 x 76
= 380
Answer(s): 380