PSLETina had two strings of the same length. She cut the first string into equal parts of length 60 cm and to each part she tied 2 white cartoon cutouts. After that, she cut the second string into equal parts of length 80 cm and to each part she tied 4 black cartoon cutouts. When she finished tying, she counted that there were 20 more black cartoon cutouts than white cartoon cutouts. How many cartoon cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
60 cm |
80 cm |
|
|
Number of balloons tied to each part |
2 white balloons |
4 black balloons |
|
|
LCM |
240 cm |
240 cm |
|
|
Number of equal parts |
240 ÷ 60 = 4 |
240 ÷ 80 = 3 |
|
|
Number of balloons for each string per set |
4 x 2 = 8 |
4 x 3 = 12 |
12 - 8 = 4 |
8 + 12 = 20 |
LCM of 60 and 80 = 240
Number of sets of 2 white cartoon cutouts in a length of 240 cm
= 240 ÷ 60
= 4
Number of white cartoon cutouts in a length of 240 cm
= 4 x 2
= 8
Number of sets of 4 black cartoon cutouts in a length of 240 cm
= 240 ÷ 80
= 3
Number of black cartoon cutouts in a length of 240 cm
= 3 x 4
= 12
Extra number of black cartoon cutouts in a length of 240 cm
= 12 - 8
= 4
Number of sets of cartoon cutouts
= 20 ÷ 4
= 5
Total number of cartoon cutouts in one set of 240 cm of white balloons and one set of 240 cm of black balloons
= 8 + 12
= 20
Total number of cartoon cutouts of the two strings
= 5 x 20
= 100
Answer(s): 100