PSLENicole had two streamers of the same length. She cut the first streamer into equal parts of length 25 cm and to each part she tied 3 white cartoon cutouts. After that, she cut the second streamer into equal parts of length 30 cm and to each part she tied 4 black cartoon cutouts. When she finished tying, she counted that there were 10 more black cartoon cutouts than white cartoon cutouts. How many cartoon cutouts were there altogether?
|
First streamer |
Second streamer |
Difference |
Total |
Length of each part |
25 cm |
30 cm |
|
|
Number of balloons tied to each part |
3 white balloons |
4 black balloons |
|
|
LCM |
150 cm |
150 cm |
|
|
Number of equal parts |
150 ÷ 25 = 6 |
150 ÷ 30 = 5 |
|
|
Number of balloons for each streamer per set |
6 x 3 = 18 |
4 x 5 = 20 |
20 - 18 = 2 |
18 + 20 = 38 |
LCM of 25 and 30 = 150
Number of sets of 3 white cartoon cutouts in a length of 150 cm
= 150 ÷ 25
= 6
Number of white cartoon cutouts in a length of 150 cm
= 6 x 3
= 18
Number of sets of 4 black cartoon cutouts in a length of 150 cm
= 150 ÷ 30
= 5
Number of black cartoon cutouts in a length of 150 cm
= 5 x 4
= 20
Extra number of black cartoon cutouts in a length of 150 cm
= 20 - 18
= 2
Number of sets of cartoon cutouts
= 10 ÷ 2
= 5
Total number of cartoon cutouts in one set of 150 cm of white balloons and one set of 150 cm of black balloons
= 18 + 20
= 38
Total number of cartoon cutouts of the two streamers
= 5 x 38
= 190
Answer(s): 190