PSLEGem had two streamers of the same length. She cut the first streamer into equal parts of length 40 cm and to each part she tied 2 brown heart cutouts. After that, she cut the second streamer into equal parts of length 45 cm and to each part she tied 3 blue heart cutouts. When she finished tying, she counted that there were 12 more blue heart cutouts than brown heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
40 cm |
45 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
3 blue balloons |
|
|
LCM |
360 cm |
360 cm |
|
|
Number of equal parts |
360 ÷ 40 = 9 |
360 ÷ 45 = 8 |
|
|
Number of balloons for each streamer per set |
9 x 2 = 18 |
3 x 8 = 24 |
24 - 18 = 6 |
18 + 24 = 42 |
LCM of 40 and 45 = 360
Number of sets of 2 brown heart cutouts in a length of 360 cm
= 360 ÷ 40
= 9
Number of brown heart cutouts in a length of 360 cm
= 9 x 2
= 18
Number of sets of 3 blue heart cutouts in a length of 360 cm
= 360 ÷ 45
= 8
Number of blue heart cutouts in a length of 360 cm
= 8 x 3
= 24
Extra number of blue heart cutouts in a length of 360 cm
= 24 - 18
= 6
Number of sets of heart cutouts
= 12 ÷ 6
= 2
Total number of heart cutouts in one set of 360 cm of brown balloons and one set of 360 cm of blue balloons
= 18 + 24
= 42
Total number of heart cutouts of the two streamers
= 2 x 42
= 84
Answer(s): 84