PSLEAbi had two strings of the same length. She cut the first string into equal parts of length 50 cm and to each part she tied 3 brown balloons. After that, she cut the second string into equal parts of length 70 cm and to each part she tied 5 purple balloons. When she finished tying, she counted that there were 12 more purple balloons than brown balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
50 cm |
70 cm |
|
|
Number of balloons tied to each part |
3 brown balloons |
5 purple balloons |
|
|
LCM |
350 cm |
350 cm |
|
|
Number of equal parts |
350 ÷ 50 = 7 |
350 ÷ 70 = 5 |
|
|
Number of balloons for each string per set |
7 x 3 = 21 |
5 x 5 = 25 |
25 - 21 = 4 |
21 + 25 = 46 |
LCM of 50 and 70 = 350
Number of sets of 3 brown balloons in a length of 350 cm
= 350 ÷ 50
= 7
Number of brown balloons in a length of 350 cm
= 7 x 3
= 21
Number of sets of 5 purple balloons in a length of 350 cm
= 350 ÷ 70
= 5
Number of purple balloons in a length of 350 cm
= 5 x 5
= 25
Extra number of purple balloons in a length of 350 cm
= 25 - 21
= 4
Number of sets of balloons
= 12 ÷ 4
= 3
Total number of balloons in one set of 350 cm of brown balloons and one set of 350 cm of purple balloons
= 21 + 25
= 46
Total number of balloons of the two strings
= 3 x 46
= 138
Answer(s): 138