PSLEFiona had two streamers of the same length. She cut the first streamer into equal parts of length 20 cm and to each part she tied 2 gold balloons. After that, she cut the second streamer into equal parts of length 45 cm and to each part she tied 5 grey balloons. When she finished tying, she counted that there were 4 more grey balloons than gold balloons. How many balloons were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
20 cm |
45 cm |
|
|
Number of balloons tied to each part |
2 gold balloons |
5 grey balloons |
|
|
LCM |
180 cm |
180 cm |
|
|
Number of equal parts |
180 ÷ 20 = 9 |
180 ÷ 45 = 4 |
|
|
Number of balloons for each streamer per set |
9 x 2 = 18 |
5 x 4 = 20 |
20 - 18 = 2 |
18 + 20 = 38 |
LCM of 20 and 45 = 180
Number of sets of 2 gold balloons in a length of 180 cm
= 180 ÷ 20
= 9
Number of gold balloons in a length of 180 cm
= 9 x 2
= 18
Number of sets of 5 grey balloons in a length of 180 cm
= 180 ÷ 45
= 4
Number of grey balloons in a length of 180 cm
= 4 x 5
= 20
Extra number of grey balloons in a length of 180 cm
= 20 - 18
= 2
Number of sets of balloons
= 4 ÷ 2
= 2
Total number of balloons in one set of 180 cm of gold balloons and one set of 180 cm of grey balloons
= 18 + 20
= 38
Total number of balloons of the two streamers
= 2 x 38
= 76
Answer(s): 76