PSLEHilda 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 3 green stars. After that, she cut the second streamer into equal parts of length 100 cm and to each part she tied 4 gold stars. When she finished tying, she counted that there were 12 more gold stars than green 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 |
3 green balloons |
4 gold 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 3 = 30 |
4 x 9 = 36 |
36 - 30 = 6 |
30 + 36 = 66 |
LCM of 90 and 100 = 900
Number of sets of 3 green stars in a length of 900 cm
= 900 ÷ 90
= 10
Number of green stars in a length of 900 cm
= 10 x 3
= 30
Number of sets of 4 gold stars in a length of 900 cm
= 900 ÷ 100
= 9
Number of gold stars in a length of 900 cm
= 9 x 4
= 36
Extra number of gold stars in a length of 900 cm
= 36 - 30
= 6
Number of sets of stars
= 12 ÷ 6
= 2
Total number of stars in one set of 900 cm of green balloons and one set of 900 cm of gold balloons
= 30 + 36
= 66
Total number of stars of the two streamers
= 2 x 66
= 132
Answer(s): 132