PSLEKimberly had two ribbons of the same length. She cut the first ribbon into equal parts of length 90 cm and to each part she tied 3 grey cartoon cutouts. After that, she cut the second ribbon into equal parts of length 100 cm and to each part she tied 4 black cartoon cutouts. When she finished tying, she counted that there were 24 more black cartoon cutouts than grey cartoon cutouts. How many cartoon cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
90 cm |
100 cm |
|
|
Number of balloons tied to each part |
3 grey balloons |
4 black balloons |
|
|
LCM |
900 cm |
900 cm |
|
|
Number of equal parts |
900 ÷ 90 = 10 |
900 ÷ 100 = 9 |
|
|
Number of balloons for each ribbon per set |
10 x 3 = 30 |
4 x 9 = 36 |
36 - 30 = 6 |
30 + 36 = 66 |
LCM of 90 and 100 = 900
Number of sets of 3 grey cartoon cutouts in a length of 900 cm
= 900 ÷ 90
= 10
Number of grey cartoon cutouts in a length of 900 cm
= 10 x 3
= 30
Number of sets of 4 black cartoon cutouts in a length of 900 cm
= 900 ÷ 100
= 9
Number of black cartoon cutouts in a length of 900 cm
= 9 x 4
= 36
Extra number of black cartoon cutouts in a length of 900 cm
= 36 - 30
= 6
Number of sets of cartoon cutouts
= 24 ÷ 6
= 4
Total number of cartoon cutouts in one set of 900 cm of grey balloons and one set of 900 cm of black balloons
= 30 + 36
= 66
Total number of cartoon cutouts of the two ribbons
= 4 x 66
= 264
Answer(s): 264