PSLEVanessa 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 3 red cartoon cutouts. After that, she cut the second streamer into equal parts of length 40 cm and to each part she tied 4 grey cartoon cutouts. When she finished tying, she counted that there were 20 more grey cartoon cutouts than red cartoon cutouts. How many cartoon 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 |
3 red balloons |
4 grey 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 3 = 24 |
4 x 7 = 28 |
28 - 24 = 4 |
24 + 28 = 52 |
LCM of 35 and 40 = 280
Number of sets of 3 red cartoon cutouts in a length of 280 cm
= 280 ÷ 35
= 8
Number of red cartoon cutouts in a length of 280 cm
= 8 x 3
= 24
Number of sets of 4 grey cartoon cutouts in a length of 280 cm
= 280 ÷ 40
= 7
Number of grey cartoon cutouts in a length of 280 cm
= 7 x 4
= 28
Extra number of grey cartoon cutouts in a length of 280 cm
= 28 - 24
= 4
Number of sets of cartoon cutouts
= 20 ÷ 4
= 5
Total number of cartoon cutouts in one set of 280 cm of red balloons and one set of 280 cm of grey balloons
= 24 + 28
= 52
Total number of cartoon cutouts of the two streamers
= 5 x 52
= 260
Answer(s): 260