PSLEAbi had two strings of the same length. She cut the first string into equal parts of length 40 cm and to each part she tied 2 purple balloons. After that, she cut the second string into equal parts of length 90 cm and to each part she tied 5 pink balloons. When she finished tying, she counted that there were 10 more pink balloons than purple balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
40 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 purple balloons |
5 pink balloons |
|
|
LCM |
360 cm |
360 cm |
|
|
Number of equal parts |
360 ÷ 40 = 9 |
360 ÷ 90 = 4 |
|
|
Number of balloons for each string per set |
9 x 2 = 18 |
5 x 4 = 20 |
20 - 18 = 2 |
18 + 20 = 38 |
LCM of 40 and 90 = 360
Number of sets of 2 purple balloons in a length of 360 cm
= 360 ÷ 40
= 9
Number of purple balloons in a length of 360 cm
= 9 x 2
= 18
Number of sets of 5 pink balloons in a length of 360 cm
= 360 ÷ 90
= 4
Number of pink balloons in a length of 360 cm
= 4 x 5
= 20
Extra number of pink balloons in a length of 360 cm
= 20 - 18
= 2
Number of sets of balloons
= 10 ÷ 2
= 5
Total number of balloons in one set of 360 cm of purple balloons and one set of 360 cm of pink balloons
= 18 + 20
= 38
Total number of balloons of the two strings
= 5 x 38
= 190
Answer(s): 190