PSLEDana had two streamers of the same length. She cut the first streamer into equal parts of length 45 cm and to each part she tied 2 black balloons. After that, she cut the second streamer into equal parts of length 50 cm and to each part she tied 5 yellow balloons. When she finished tying, she counted that there were 125 more yellow balloons than black balloons. How many balloons were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
45 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 black balloons |
5 yellow balloons |
|
|
LCM |
450 cm |
450 cm |
|
|
Number of equal parts |
450 ÷ 45 = 10 |
450 ÷ 50 = 9 |
|
|
Number of balloons for each streamer per set |
10 x 2 = 20 |
5 x 9 = 45 |
45 - 20 = 25 |
20 + 45 = 65 |
LCM of 45 and 50 = 450
Number of sets of 2 black balloons in a length of 450 cm
= 450 ÷ 45
= 10
Number of black balloons in a length of 450 cm
= 10 x 2
= 20
Number of sets of 5 yellow balloons in a length of 450 cm
= 450 ÷ 50
= 9
Number of yellow balloons in a length of 450 cm
= 9 x 5
= 45
Extra number of yellow balloons in a length of 450 cm
= 45 - 20
= 25
Number of sets of balloons
= 125 ÷ 25
= 5
Total number of balloons in one set of 450 cm of black balloons and one set of 450 cm of yellow balloons
= 20 + 45
= 65
Total number of balloons of the two streamers
= 5 x 65
= 325
Answer(s): 325