PSLEJoelle had two streamers of the same length. She cut the first streamer into equal parts of length 70 cm and to each part she tied 2 pink balls. After that, she cut the second streamer into equal parts of length 90 cm and to each part she tied 5 black balls. When she finished tying, she counted that there were 34 more black balls than pink balls. How many balls were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
70 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 pink balloons |
5 black balloons |
|
|
LCM |
630 cm |
630 cm |
|
|
Number of equal parts |
630 ÷ 70 = 9 |
630 ÷ 90 = 7 |
|
|
Number of balloons for each streamer per set |
9 x 2 = 18 |
5 x 7 = 35 |
35 - 18 = 17 |
18 + 35 = 53 |
LCM of 70 and 90 = 630
Number of sets of 2 pink balls in a length of 630 cm
= 630 ÷ 70
= 9
Number of pink balls in a length of 630 cm
= 9 x 2
= 18
Number of sets of 5 black balls in a length of 630 cm
= 630 ÷ 90
= 7
Number of black balls in a length of 630 cm
= 7 x 5
= 35
Extra number of black balls in a length of 630 cm
= 35 - 18
= 17
Number of sets of balls
= 34 ÷ 17
= 2
Total number of balls in one set of 630 cm of pink balloons and one set of 630 cm of black balloons
= 18 + 35
= 53
Total number of balls of the two streamers
= 2 x 53
= 106
Answer(s): 106