PSLEFanny had two streamers of the same length. She cut the first streamer into equal parts of length 60 cm and to each part she tied 3 blue heart cutouts. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 5 grey heart cutouts. When she finished tying, she counted that there were 15 more grey heart cutouts than blue heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
60 cm |
80 cm |
|
|
Number of balloons tied to each part |
3 blue balloons |
5 grey balloons |
|
|
LCM |
240 cm |
240 cm |
|
|
Number of equal parts |
240 ÷ 60 = 4 |
240 ÷ 80 = 3 |
|
|
Number of balloons for each streamer per set |
4 x 3 = 12 |
5 x 3 = 15 |
15 - 12 = 3 |
12 + 15 = 27 |
LCM of 60 and 80 = 240
Number of sets of 3 blue heart cutouts in a length of 240 cm
= 240 ÷ 60
= 4
Number of blue heart cutouts in a length of 240 cm
= 4 x 3
= 12
Number of sets of 5 grey heart cutouts in a length of 240 cm
= 240 ÷ 80
= 3
Number of grey heart cutouts in a length of 240 cm
= 3 x 5
= 15
Extra number of grey heart cutouts in a length of 240 cm
= 15 - 12
= 3
Number of sets of heart cutouts
= 15 ÷ 3
= 5
Total number of heart cutouts in one set of 240 cm of blue balloons and one set of 240 cm of grey balloons
= 12 + 15
= 27
Total number of heart cutouts of the two streamers
= 5 x 27
= 135
Answer(s): 135