PSLETiffany 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 blue cartoon cutouts. After that, she cut the second streamer into equal parts of length 45 cm and to each part she tied 4 red cartoon cutouts. When she finished tying, she counted that there were 30 more red cartoon cutouts than blue cartoon cutouts. How many cartoon cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
35 cm |
45 cm |
|
|
Number of balloons tied to each part |
2 blue balloons |
4 red balloons |
|
|
LCM |
315 cm |
315 cm |
|
|
Number of equal parts |
315 ÷ 35 = 9 |
315 ÷ 45 = 7 |
|
|
Number of balloons for each streamer per set |
9 x 2 = 18 |
4 x 7 = 28 |
28 - 18 = 10 |
18 + 28 = 46 |
LCM of 35 and 45 = 315
Number of sets of 2 blue cartoon cutouts in a length of 315 cm
= 315 ÷ 35
= 9
Number of blue cartoon cutouts in a length of 315 cm
= 9 x 2
= 18
Number of sets of 4 red cartoon cutouts in a length of 315 cm
= 315 ÷ 45
= 7
Number of red cartoon cutouts in a length of 315 cm
= 7 x 4
= 28
Extra number of red cartoon cutouts in a length of 315 cm
= 28 - 18
= 10
Number of sets of cartoon cutouts
= 30 ÷ 10
= 3
Total number of cartoon cutouts in one set of 315 cm of blue balloons and one set of 315 cm of red balloons
= 18 + 28
= 46
Total number of cartoon cutouts of the two streamers
= 3 x 46
= 138
Answer(s): 138