PSLESabrina had two streamers of the same length. She cut the first streamer into equal parts of length 80 cm and to each part she tied 3 blue heart cutouts. After that, she cut the second streamer into equal parts of length 90 cm and to each part she tied 4 yellow heart cutouts. When she finished tying, she counted that there were 20 more yellow heart cutouts than blue heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
80 cm |
90 cm |
|
|
Number of balloons tied to each part |
3 blue balloons |
4 yellow balloons |
|
|
LCM |
720 cm |
720 cm |
|
|
Number of equal parts |
720 ÷ 80 = 9 |
720 ÷ 90 = 8 |
|
|
Number of balloons for each streamer per set |
9 x 3 = 27 |
4 x 8 = 32 |
32 - 27 = 5 |
27 + 32 = 59 |
LCM of 80 and 90 = 720
Number of sets of 3 blue heart cutouts in a length of 720 cm
= 720 ÷ 80
= 9
Number of blue heart cutouts in a length of 720 cm
= 9 x 3
= 27
Number of sets of 4 yellow heart cutouts in a length of 720 cm
= 720 ÷ 90
= 8
Number of yellow heart cutouts in a length of 720 cm
= 8 x 4
= 32
Extra number of yellow heart cutouts in a length of 720 cm
= 32 - 27
= 5
Number of sets of heart cutouts
= 20 ÷ 5
= 4
Total number of heart cutouts in one set of 720 cm of blue balloons and one set of 720 cm of yellow balloons
= 27 + 32
= 59
Total number of heart cutouts of the two streamers
= 4 x 59
= 236
Answer(s): 236