PSLEJean 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 gold cartoon cutouts. After that, she cut the second string into equal parts of length 80 cm and to each part she tied 5 blue cartoon cutouts. When she finished tying, she counted that there were 28 more blue cartoon cutouts than gold 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 gold balloons |
5 blue 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 |
5 x 3 = 15 |
15 - 8 = 7 |
8 + 15 = 23 |
LCM of 60 and 80 = 240
Number of sets of 2 gold cartoon cutouts in a length of 240 cm
= 240 ÷ 60
= 4
Number of gold cartoon cutouts in a length of 240 cm
= 4 x 2
= 8
Number of sets of 5 blue cartoon cutouts in a length of 240 cm
= 240 ÷ 80
= 3
Number of blue cartoon cutouts in a length of 240 cm
= 3 x 5
= 15
Extra number of blue cartoon cutouts in a length of 240 cm
= 15 - 8
= 7
Number of sets of cartoon cutouts
= 28 ÷ 7
= 4
Total number of cartoon cutouts in one set of 240 cm of gold balloons and one set of 240 cm of blue balloons
= 8 + 15
= 23
Total number of cartoon cutouts of the two strings
= 4 x 23
= 92
Answer(s): 92