PSLETina had two strings of the same length. She cut the first string into equal parts of length 20 cm and to each part she tied 2 grey cartoon cutouts. After that, she cut the second string into equal parts of length 25 cm and to each part she tied 3 blue cartoon cutouts. When she finished tying, she counted that there were 6 more blue cartoon cutouts than grey cartoon cutouts. How many cartoon cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
20 cm |
25 cm |
|
|
Number of balloons tied to each part |
2 grey balloons |
3 blue balloons |
|
|
LCM |
100 cm |
100 cm |
|
|
Number of equal parts |
100 ÷ 20 = 5 |
100 ÷ 25 = 4 |
|
|
Number of balloons for each string per set |
5 x 2 = 10 |
3 x 4 = 12 |
12 - 10 = 2 |
10 + 12 = 22 |
LCM of 20 and 25 = 100
Number of sets of 2 grey cartoon cutouts in a length of 100 cm
= 100 ÷ 20
= 5
Number of grey cartoon cutouts in a length of 100 cm
= 5 x 2
= 10
Number of sets of 3 blue cartoon cutouts in a length of 100 cm
= 100 ÷ 25
= 4
Number of blue cartoon cutouts in a length of 100 cm
= 4 x 3
= 12
Extra number of blue cartoon cutouts in a length of 100 cm
= 12 - 10
= 2
Number of sets of cartoon cutouts
= 6 ÷ 2
= 3
Total number of cartoon cutouts in one set of 100 cm of grey balloons and one set of 100 cm of blue balloons
= 10 + 12
= 22
Total number of cartoon cutouts of the two strings
= 3 x 22
= 66
Answer(s): 66