PSLEGabby had two streamers of the same length. She cut the first streamer into equal parts of length 70 cm and to each part she tied 3 green heart cutouts. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 5 blue heart cutouts. When she finished tying, she counted that there were 44 more blue heart cutouts than green heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
70 cm |
80 cm |
|
|
Number of balloons tied to each part |
3 green balloons |
5 blue balloons |
|
|
LCM |
560 cm |
560 cm |
|
|
Number of equal parts |
560 ÷ 70 = 8 |
560 ÷ 80 = 7 |
|
|
Number of balloons for each streamer per set |
8 x 3 = 24 |
5 x 7 = 35 |
35 - 24 = 11 |
24 + 35 = 59 |
LCM of 70 and 80 = 560
Number of sets of 3 green heart cutouts in a length of 560 cm
= 560 ÷ 70
= 8
Number of green heart cutouts in a length of 560 cm
= 8 x 3
= 24
Number of sets of 5 blue heart cutouts in a length of 560 cm
= 560 ÷ 80
= 7
Number of blue heart cutouts in a length of 560 cm
= 7 x 5
= 35
Extra number of blue heart cutouts in a length of 560 cm
= 35 - 24
= 11
Number of sets of heart cutouts
= 44 ÷ 11
= 4
Total number of heart cutouts in one set of 560 cm of green balloons and one set of 560 cm of blue balloons
= 24 + 35
= 59
Total number of heart cutouts of the two streamers
= 4 x 59
= 236
Answer(s): 236