PSLEOlivium had two streamers of the same length. She cut the first streamer into equal parts of length 35 cm and to each part she tied 2 white heart cutouts. After that, she cut the second streamer into equal parts of length 40 cm and to each part she tied 5 red heart cutouts. When she finished tying, she counted that there were 95 more red heart cutouts than white heart cutouts. How many heart cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
35 cm |
40 cm |
|
|
Number of balloons tied to each part |
2 white balloons |
5 red balloons |
|
|
LCM |
280 cm |
280 cm |
|
|
Number of equal parts |
280 ÷ 35 = 8 |
280 ÷ 40 = 7 |
|
|
Number of balloons for each streamer per set |
8 x 2 = 16 |
5 x 7 = 35 |
35 - 16 = 19 |
16 + 35 = 51 |
LCM of 35 and 40 = 280
Number of sets of 2 white heart cutouts in a length of 280 cm
= 280 ÷ 35
= 8
Number of white heart cutouts in a length of 280 cm
= 8 x 2
= 16
Number of sets of 5 red heart cutouts in a length of 280 cm
= 280 ÷ 40
= 7
Number of red heart cutouts in a length of 280 cm
= 7 x 5
= 35
Extra number of red heart cutouts in a length of 280 cm
= 35 - 16
= 19
Number of sets of heart cutouts
= 95 ÷ 19
= 5
Total number of heart cutouts in one set of 280 cm of white balloons and one set of 280 cm of red balloons
= 16 + 35
= 51
Total number of heart cutouts of the two streamers
= 5 x 51
= 255
Answer(s): 255