PSLEFiona had two strings of the same length. She cut the first string into equal parts of length 30 cm and to each part she tied 3 green balls. After that, she cut the second string into equal parts of length 35 cm and to each part she tied 5 silver balls. When she finished tying, she counted that there were 18 more silver balls than green balls. How many balls were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
30 cm |
35 cm |
|
|
Number of balloons tied to each part |
3 green balloons |
5 silver balloons |
|
|
LCM |
210 cm |
210 cm |
|
|
Number of equal parts |
210 ÷ 30 = 7 |
210 ÷ 35 = 6 |
|
|
Number of balloons for each string per set |
7 x 3 = 21 |
5 x 6 = 30 |
30 - 21 = 9 |
21 + 30 = 51 |
LCM of 30 and 35 = 210
Number of sets of 3 green balls in a length of 210 cm
= 210 ÷ 30
= 7
Number of green balls in a length of 210 cm
= 7 x 3
= 21
Number of sets of 5 silver balls in a length of 210 cm
= 210 ÷ 35
= 6
Number of silver balls in a length of 210 cm
= 6 x 5
= 30
Extra number of silver balls in a length of 210 cm
= 30 - 21
= 9
Number of sets of balls
= 18 ÷ 9
= 2
Total number of balls in one set of 210 cm of green balloons and one set of 210 cm of silver balloons
= 21 + 30
= 51
Total number of balls of the two strings
= 2 x 51
= 102
Answer(s): 102