PSLEBetty had two strings of the same length. She cut the first string into equal parts of length 80 cm and to each part she tied 2 brown stars. After that, she cut the second string into equal parts of length 90 cm and to each part she tied 4 green stars. When she finished tying, she counted that there were 42 more green stars than brown stars. How many stars were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
80 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
4 green balloons |
|
|
LCM |
720 cm |
720 cm |
|
|
Number of equal parts |
720 ÷ 80 = 9 |
720 ÷ 90 = 8 |
|
|
Number of balloons for each string per set |
9 x 2 = 18 |
4 x 8 = 32 |
32 - 18 = 14 |
18 + 32 = 50 |
LCM of 80 and 90 = 720
Number of sets of 2 brown stars in a length of 720 cm
= 720 ÷ 80
= 9
Number of brown stars in a length of 720 cm
= 9 x 2
= 18
Number of sets of 4 green stars in a length of 720 cm
= 720 ÷ 90
= 8
Number of green stars in a length of 720 cm
= 8 x 4
= 32
Extra number of green stars in a length of 720 cm
= 32 - 18
= 14
Number of sets of stars
= 42 ÷ 14
= 3
Total number of stars in one set of 720 cm of brown balloons and one set of 720 cm of green balloons
= 18 + 32
= 50
Total number of stars of the two strings
= 3 x 50
= 150
Answer(s): 150