PSLENicole had two ribbons of the same length. She cut the first ribbon into equal parts of length 30 cm and to each part she tied 2 blue cartoon cutouts. After that, she cut the second ribbon into equal parts of length 50 cm and to each part she tied 4 green cartoon cutouts. When she finished tying, she counted that there were 4 more green cartoon cutouts than blue cartoon cutouts. How many cartoon cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
30 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 blue balloons |
4 green balloons |
|
|
LCM |
150 cm |
150 cm |
|
|
Number of equal parts |
150 ÷ 30 = 5 |
150 ÷ 50 = 3 |
|
|
Number of balloons for each ribbon per set |
5 x 2 = 10 |
4 x 3 = 12 |
12 - 10 = 2 |
10 + 12 = 22 |
LCM of 30 and 50 = 150
Number of sets of 2 blue cartoon cutouts in a length of 150 cm
= 150 ÷ 30
= 5
Number of blue cartoon cutouts in a length of 150 cm
= 5 x 2
= 10
Number of sets of 4 green cartoon cutouts in a length of 150 cm
= 150 ÷ 50
= 3
Number of green cartoon cutouts in a length of 150 cm
= 3 x 4
= 12
Extra number of green cartoon cutouts in a length of 150 cm
= 12 - 10
= 2
Number of sets of cartoon cutouts
= 4 ÷ 2
= 2
Total number of cartoon cutouts in one set of 150 cm of blue balloons and one set of 150 cm of green balloons
= 10 + 12
= 22
Total number of cartoon cutouts of the two ribbons
= 2 x 22
= 44
Answer(s): 44