PSLEJade 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 2 blue balls. After that, she cut the second streamer into equal parts of length 70 cm and to each part she tied 5 red balls. When she finished tying, she counted that there were 48 more red balls than blue 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 |
2 blue balloons |
5 red 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 2 = 14 |
5 x 6 = 30 |
30 - 14 = 16 |
14 + 30 = 44 |
LCM of 60 and 70 = 420
Number of sets of 2 blue balls in a length of 420 cm
= 420 ÷ 60
= 7
Number of blue balls in a length of 420 cm
= 7 x 2
= 14
Number of sets of 5 red balls in a length of 420 cm
= 420 ÷ 70
= 6
Number of red balls in a length of 420 cm
= 6 x 5
= 30
Extra number of red balls in a length of 420 cm
= 30 - 14
= 16
Number of sets of balls
= 48 ÷ 16
= 3
Total number of balls in one set of 420 cm of blue balloons and one set of 420 cm of red balloons
= 14 + 30
= 44
Total number of balls of the two streamers
= 3 x 44
= 132
Answer(s): 132