PSLERoshel 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 2 blue heart cutouts. After that, she cut the second streamer into equal parts of length 90 cm and to each part she tied 5 gold heart cutouts. When she finished tying, she counted that there were 66 more gold 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 |
2 blue balloons |
5 gold 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 2 = 18 |
5 x 8 = 40 |
40 - 18 = 22 |
18 + 40 = 58 |
LCM of 80 and 90 = 720
Number of sets of 2 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 2
= 18
Number of sets of 5 gold heart cutouts in a length of 720 cm
= 720 ÷ 90
= 8
Number of gold heart cutouts in a length of 720 cm
= 8 x 5
= 40
Extra number of gold heart cutouts in a length of 720 cm
= 40 - 18
= 22
Number of sets of heart cutouts
= 66 ÷ 22
= 3
Total number of heart cutouts in one set of 720 cm of blue balloons and one set of 720 cm of gold balloons
= 18 + 40
= 58
Total number of heart cutouts of the two streamers
= 3 x 58
= 174
Answer(s): 174