PSLEGem had two ribbons of the same length. She cut the first ribbon into equal parts of length 45 cm and to each part she tied 2 purple balls. After that, she cut the second ribbon into equal parts of length 50 cm and to each part she tied 3 brown balls. When she finished tying, she counted that there were 21 more brown balls than purple balls. How many balls were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
45 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 purple balloons |
3 brown balloons |
|
|
LCM |
450 cm |
450 cm |
|
|
Number of equal parts |
450 ÷ 45 = 10 |
450 ÷ 50 = 9 |
|
|
Number of balloons for each ribbon per set |
10 x 2 = 20 |
3 x 9 = 27 |
27 - 20 = 7 |
20 + 27 = 47 |
LCM of 45 and 50 = 450
Number of sets of 2 purple balls in a length of 450 cm
= 450 ÷ 45
= 10
Number of purple balls in a length of 450 cm
= 10 x 2
= 20
Number of sets of 3 brown balls in a length of 450 cm
= 450 ÷ 50
= 9
Number of brown balls in a length of 450 cm
= 9 x 3
= 27
Extra number of brown balls in a length of 450 cm
= 27 - 20
= 7
Number of sets of balls
= 21 ÷ 7
= 3
Total number of balls in one set of 450 cm of purple balloons and one set of 450 cm of brown balloons
= 20 + 27
= 47
Total number of balls of the two ribbons
= 3 x 47
= 141
Answer(s): 141