PSLEGwen had two strings of the same length. She cut the first string into equal parts of length 25 cm and to each part she tied 2 blue cartoon cutouts. After that, she cut the second string into equal parts of length 45 cm and to each part she tied 5 black cartoon cutouts. When she finished tying, she counted that there were 21 more black cartoon cutouts than blue cartoon cutouts. How many cartoon cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
25 cm |
45 cm |
|
|
Number of balloons tied to each part |
2 blue balloons |
5 black balloons |
|
|
LCM |
225 cm |
225 cm |
|
|
Number of equal parts |
225 ÷ 25 = 9 |
225 ÷ 45 = 5 |
|
|
Number of balloons for each string per set |
9 x 2 = 18 |
5 x 5 = 25 |
25 - 18 = 7 |
18 + 25 = 43 |
LCM of 25 and 45 = 225
Number of sets of 2 blue cartoon cutouts in a length of 225 cm
= 225 ÷ 25
= 9
Number of blue cartoon cutouts in a length of 225 cm
= 9 x 2
= 18
Number of sets of 5 black cartoon cutouts in a length of 225 cm
= 225 ÷ 45
= 5
Number of black cartoon cutouts in a length of 225 cm
= 5 x 5
= 25
Extra number of black cartoon cutouts in a length of 225 cm
= 25 - 18
= 7
Number of sets of cartoon cutouts
= 21 ÷ 7
= 3
Total number of cartoon cutouts in one set of 225 cm of blue balloons and one set of 225 cm of black balloons
= 18 + 25
= 43
Total number of cartoon cutouts of the two strings
= 3 x 43
= 129
Answer(s): 129