PSLESarah 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 3 silver cartoon cutouts. After that, she cut the second streamer into equal parts of length 90 cm and to each part she tied 4 red cartoon cutouts. When she finished tying, she counted that there were 15 more red cartoon cutouts than silver cartoon cutouts. How many cartoon 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 |
3 silver balloons |
4 red 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 3 = 27 |
4 x 8 = 32 |
32 - 27 = 5 |
27 + 32 = 59 |
LCM of 80 and 90 = 720
Number of sets of 3 silver cartoon cutouts in a length of 720 cm
= 720 ÷ 80
= 9
Number of silver cartoon cutouts in a length of 720 cm
= 9 x 3
= 27
Number of sets of 4 red cartoon cutouts in a length of 720 cm
= 720 ÷ 90
= 8
Number of red cartoon cutouts in a length of 720 cm
= 8 x 4
= 32
Extra number of red cartoon cutouts in a length of 720 cm
= 32 - 27
= 5
Number of sets of cartoon cutouts
= 15 ÷ 5
= 3
Total number of cartoon cutouts in one set of 720 cm of silver balloons and one set of 720 cm of red balloons
= 27 + 32
= 59
Total number of cartoon cutouts of the two streamers
= 3 x 59
= 177
Answer(s): 177