PSLENatalie had two streamers of the same length. She cut the first streamer into equal parts of length 60 cm and to each part she tied 3 black balls. After that, she cut the second streamer into equal parts of length 70 cm and to each part she tied 4 purple balls. When she finished tying, she counted that there were 9 more purple balls than black balls. How many balls were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
60 cm |
70 cm |
|
|
Number of balloons tied to each part |
3 black balloons |
4 purple balloons |
|
|
LCM |
420 cm |
420 cm |
|
|
Number of equal parts |
420 ÷ 60 = 7 |
420 ÷ 70 = 6 |
|
|
Number of balloons for each streamer per set |
7 x 3 = 21 |
4 x 6 = 24 |
24 - 21 = 3 |
21 + 24 = 45 |
LCM of 60 and 70 = 420
Number of sets of 3 black balls in a length of 420 cm
= 420 ÷ 60
= 7
Number of black balls in a length of 420 cm
= 7 x 3
= 21
Number of sets of 4 purple balls in a length of 420 cm
= 420 ÷ 70
= 6
Number of purple balls in a length of 420 cm
= 6 x 4
= 24
Extra number of purple balls in a length of 420 cm
= 24 - 21
= 3
Number of sets of balls
= 9 ÷ 3
= 3
Total number of balls in one set of 420 cm of black balloons and one set of 420 cm of purple balloons
= 21 + 24
= 45
Total number of balls of the two streamers
= 3 x 45
= 135
Answer(s): 135