PSLEOlivium 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 4 white balls. After that, she cut the second string into equal parts of length 70 cm and to each part she tied 5 yellow balls. When she finished tying, she counted that there were 8 more yellow balls than white balls. How many balls were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
60 cm |
70 cm |
|
|
Number of balloons tied to each part |
4 white balloons |
5 yellow balloons |
|
|
LCM |
420 cm |
420 cm |
|
|
Number of equal parts |
420 ÷ 60 = 7 |
420 ÷ 70 = 6 |
|
|
Number of balloons for each string per set |
7 x 4 = 28 |
5 x 6 = 30 |
30 - 28 = 2 |
28 + 30 = 58 |
LCM of 60 and 70 = 420
Number of sets of 4 white balls in a length of 420 cm
= 420 ÷ 60
= 7
Number of white balls in a length of 420 cm
= 7 x 4
= 28
Number of sets of 5 yellow balls in a length of 420 cm
= 420 ÷ 70
= 6
Number of yellow balls in a length of 420 cm
= 6 x 5
= 30
Extra number of yellow balls in a length of 420 cm
= 30 - 28
= 2
Number of sets of balls
= 8 ÷ 2
= 4
Total number of balls in one set of 420 cm of white balloons and one set of 420 cm of yellow balloons
= 28 + 30
= 58
Total number of balls of the two strings
= 4 x 58
= 232
Answer(s): 232