PSLEAnna had two streamers of the same length. She cut the first streamer into equal parts of length 50 cm and to each part she tied 2 brown heart cutouts. After that, she cut the second streamer into equal parts of length 60 cm and to each part she tied 5 gold heart cutouts. When she finished tying, she counted that there were 52 more gold heart cutouts than brown heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
50 cm |
60 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
5 gold balloons |
|
|
LCM |
300 cm |
300 cm |
|
|
Number of equal parts |
300 ÷ 50 = 6 |
300 ÷ 60 = 5 |
|
|
Number of balloons for each streamer per set |
6 x 2 = 12 |
5 x 5 = 25 |
25 - 12 = 13 |
12 + 25 = 37 |
LCM of 50 and 60 = 300
Number of sets of 2 brown heart cutouts in a length of 300 cm
= 300 ÷ 50
= 6
Number of brown heart cutouts in a length of 300 cm
= 6 x 2
= 12
Number of sets of 5 gold heart cutouts in a length of 300 cm
= 300 ÷ 60
= 5
Number of gold heart cutouts in a length of 300 cm
= 5 x 5
= 25
Extra number of gold heart cutouts in a length of 300 cm
= 25 - 12
= 13
Number of sets of heart cutouts
= 52 ÷ 13
= 4
Total number of heart cutouts in one set of 300 cm of brown balloons and one set of 300 cm of gold balloons
= 12 + 25
= 37
Total number of heart cutouts of the two streamers
= 4 x 37
= 148
Answer(s): 148