PSLEJoelle had two streamers of the same length. She cut the first streamer into equal parts of length 40 cm and to each part she tied 2 white balls. After that, she cut the second streamer into equal parts of length 45 cm and to each part she tied 5 brown balls. When she finished tying, she counted that there were 66 more brown balls than white balls. How many balls were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
40 cm |
45 cm |
|
|
Number of balloons tied to each part |
2 white balloons |
5 brown balloons |
|
|
LCM |
360 cm |
360 cm |
|
|
Number of equal parts |
360 ÷ 40 = 9 |
360 ÷ 45 = 8 |
|
|
Number of balloons for each streamer per set |
9 x 2 = 18 |
5 x 8 = 40 |
40 - 18 = 22 |
18 + 40 = 58 |
LCM of 40 and 45 = 360
Number of sets of 2 white balls in a length of 360 cm
= 360 ÷ 40
= 9
Number of white balls in a length of 360 cm
= 9 x 2
= 18
Number of sets of 5 brown balls in a length of 360 cm
= 360 ÷ 45
= 8
Number of brown balls in a length of 360 cm
= 8 x 5
= 40
Extra number of brown balls in a length of 360 cm
= 40 - 18
= 22
Number of sets of balls
= 66 ÷ 22
= 3
Total number of balls in one set of 360 cm of white balloons and one set of 360 cm of brown balloons
= 18 + 40
= 58
Total number of balls of the two streamers
= 3 x 58
= 174
Answer(s): 174