PSLEGabby had two strings of the same length. She cut the first string into equal parts of length 30 cm and to each part she tied 2 green stars. After that, she cut the second string into equal parts of length 50 cm and to each part she tied 5 purple stars. When she finished tying, she counted that there were 15 more purple stars than green stars. How many stars were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
30 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 green balloons |
5 purple balloons |
|
|
LCM |
150 cm |
150 cm |
|
|
Number of equal parts |
150 ÷ 30 = 5 |
150 ÷ 50 = 3 |
|
|
Number of balloons for each string per set |
5 x 2 = 10 |
5 x 3 = 15 |
15 - 10 = 5 |
10 + 15 = 25 |
LCM of 30 and 50 = 150
Number of sets of 2 green stars in a length of 150 cm
= 150 ÷ 30
= 5
Number of green stars in a length of 150 cm
= 5 x 2
= 10
Number of sets of 5 purple stars in a length of 150 cm
= 150 ÷ 50
= 3
Number of purple stars in a length of 150 cm
= 3 x 5
= 15
Extra number of purple stars in a length of 150 cm
= 15 - 10
= 5
Number of sets of stars
= 15 ÷ 5
= 3
Total number of stars in one set of 150 cm of green balloons and one set of 150 cm of purple balloons
= 10 + 15
= 25
Total number of stars of the two strings
= 3 x 25
= 75
Answer(s): 75