PSLESabrina 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 2 brown heart cutouts. After that, she cut the second streamer into equal parts of length 100 cm and to each part she tied 4 green heart cutouts. When she finished tying, she counted that there were 32 more green heart cutouts than brown heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
70 cm |
100 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
4 green balloons |
|
|
LCM |
700 cm |
700 cm |
|
|
Number of equal parts |
700 ÷ 70 = 10 |
700 ÷ 100 = 7 |
|
|
Number of balloons for each streamer per set |
10 x 2 = 20 |
4 x 7 = 28 |
28 - 20 = 8 |
20 + 28 = 48 |
LCM of 70 and 100 = 700
Number of sets of 2 brown heart cutouts in a length of 700 cm
= 700 ÷ 70
= 10
Number of brown heart cutouts in a length of 700 cm
= 10 x 2
= 20
Number of sets of 4 green heart cutouts in a length of 700 cm
= 700 ÷ 100
= 7
Number of green heart cutouts in a length of 700 cm
= 7 x 4
= 28
Extra number of green heart cutouts in a length of 700 cm
= 28 - 20
= 8
Number of sets of heart cutouts
= 32 ÷ 8
= 4
Total number of heart cutouts in one set of 700 cm of brown balloons and one set of 700 cm of green balloons
= 20 + 28
= 48
Total number of heart cutouts of the two streamers
= 4 x 48
= 192
Answer(s): 192