PSLEKimberly had two streamers of the same length. She cut the first streamer into equal parts of length 70 cm and to each part she tied 4 grey cartoon cutouts. After that, she cut the second streamer into equal parts of length 80 cm and to each part she tied 5 gold cartoon cutouts. When she finished tying, she counted that there were 9 more gold cartoon cutouts than grey cartoon cutouts. How many cartoon cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
70 cm |
80 cm |
|
|
Number of balloons tied to each part |
4 grey balloons |
5 gold balloons |
|
|
LCM |
560 cm |
560 cm |
|
|
Number of equal parts |
560 ÷ 70 = 8 |
560 ÷ 80 = 7 |
|
|
Number of balloons for each streamer per set |
8 x 4 = 32 |
5 x 7 = 35 |
35 - 32 = 3 |
32 + 35 = 67 |
LCM of 70 and 80 = 560
Number of sets of 4 grey cartoon cutouts in a length of 560 cm
= 560 ÷ 70
= 8
Number of grey cartoon cutouts in a length of 560 cm
= 8 x 4
= 32
Number of sets of 5 gold cartoon cutouts in a length of 560 cm
= 560 ÷ 80
= 7
Number of gold cartoon cutouts in a length of 560 cm
= 7 x 5
= 35
Extra number of gold cartoon cutouts in a length of 560 cm
= 35 - 32
= 3
Number of sets of cartoon cutouts
= 9 ÷ 3
= 3
Total number of cartoon cutouts in one set of 560 cm of grey balloons and one set of 560 cm of gold balloons
= 32 + 35
= 67
Total number of cartoon cutouts of the two streamers
= 3 x 67
= 201
Answer(s): 201