PSLEGem 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 3 pink cartoon cutouts. After that, she cut the second string into equal parts of length 80 cm and to each part she tied 5 white cartoon cutouts. When she finished tying, she counted that there were 9 more white cartoon cutouts than pink 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 |
3 pink balloons |
5 white 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 3 = 12 |
5 x 3 = 15 |
15 - 12 = 3 |
12 + 15 = 27 |
LCM of 60 and 80 = 240
Number of sets of 3 pink cartoon cutouts in a length of 240 cm
= 240 ÷ 60
= 4
Number of pink cartoon cutouts in a length of 240 cm
= 4 x 3
= 12
Number of sets of 5 white cartoon cutouts in a length of 240 cm
= 240 ÷ 80
= 3
Number of white cartoon cutouts in a length of 240 cm
= 3 x 5
= 15
Extra number of white cartoon cutouts in a length of 240 cm
= 15 - 12
= 3
Number of sets of cartoon cutouts
= 9 ÷ 3
= 3
Total number of cartoon cutouts in one set of 240 cm of pink balloons and one set of 240 cm of white balloons
= 12 + 15
= 27
Total number of cartoon cutouts of the two strings
= 3 x 27
= 81
Answer(s): 81