PSLEJean had two strings of the same length. She cut the first string into equal parts of length 20 cm and to each part she tied 3 pink flags. After that, she cut the second string into equal parts of length 25 cm and to each part she tied 5 purple flags. When she finished tying, she counted that there were 15 more purple flags than pink flags. How many flags were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
20 cm |
25 cm |
|
|
Number of balloons tied to each part |
3 pink balloons |
5 purple balloons |
|
|
LCM |
100 cm |
100 cm |
|
|
Number of equal parts |
100 ÷ 20 = 5 |
100 ÷ 25 = 4 |
|
|
Number of balloons for each string per set |
5 x 3 = 15 |
5 x 4 = 20 |
20 - 15 = 5 |
15 + 20 = 35 |
LCM of 20 and 25 = 100
Number of sets of 3 pink flags in a length of 100 cm
= 100 ÷ 20
= 5
Number of pink flags in a length of 100 cm
= 5 x 3
= 15
Number of sets of 5 purple flags in a length of 100 cm
= 100 ÷ 25
= 4
Number of purple flags in a length of 100 cm
= 4 x 5
= 20
Extra number of purple flags in a length of 100 cm
= 20 - 15
= 5
Number of sets of flags
= 15 ÷ 5
= 3
Total number of flags in one set of 100 cm of pink balloons and one set of 100 cm of purple balloons
= 15 + 20
= 35
Total number of flags of the two strings
= 3 x 35
= 105
Answer(s): 105