PSLECathy had two streamers of the same length. She cut the first streamer into equal parts of length 90 cm and to each part she tied 4 black stars. After that, she cut the second streamer into equal parts of length 100 cm and to each part she tied 5 green stars. When she finished tying, she counted that there were 20 more green stars than black stars. How many stars were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
90 cm |
100 cm |
|
|
Number of balloons tied to each part |
4 black balloons |
5 green balloons |
|
|
LCM |
900 cm |
900 cm |
|
|
Number of equal parts |
900 ÷ 90 = 10 |
900 ÷ 100 = 9 |
|
|
Number of balloons for each streamer per set |
10 x 4 = 40 |
5 x 9 = 45 |
45 - 40 = 5 |
40 + 45 = 85 |
LCM of 90 and 100 = 900
Number of sets of 4 black stars in a length of 900 cm
= 900 ÷ 90
= 10
Number of black stars in a length of 900 cm
= 10 x 4
= 40
Number of sets of 5 green stars in a length of 900 cm
= 900 ÷ 100
= 9
Number of green stars in a length of 900 cm
= 9 x 5
= 45
Extra number of green stars in a length of 900 cm
= 45 - 40
= 5
Number of sets of stars
= 20 ÷ 5
= 4
Total number of stars in one set of 900 cm of black balloons and one set of 900 cm of green balloons
= 40 + 45
= 85
Total number of stars of the two streamers
= 4 x 85
= 340
Answer(s): 340