PSLEYoko 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 grey heart cutouts. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 4 green heart cutouts. When she finished tying, she counted that there were 12 more green heart cutouts than grey 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 grey balloons |
4 green 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 |
4 x 7 = 28 |
28 - 24 = 4 |
24 + 28 = 52 |
LCM of 70 and 80 = 560
Number of sets of 3 grey heart cutouts in a length of 560 cm
= 560 ÷ 70
= 8
Number of grey heart cutouts in a length of 560 cm
= 8 x 3
= 24
Number of sets of 4 green heart cutouts in a length of 560 cm
= 560 ÷ 80
= 7
Number of green heart cutouts in a length of 560 cm
= 7 x 4
= 28
Extra number of green heart cutouts in a length of 560 cm
= 28 - 24
= 4
Number of sets of heart cutouts
= 12 ÷ 4
= 3
Total number of heart cutouts in one set of 560 cm of grey balloons and one set of 560 cm of green balloons
= 24 + 28
= 52
Total number of heart cutouts of the two streamers
= 3 x 52
= 156
Answer(s): 156