PSLEJean had two ribbons of the same length. She cut the first ribbon into equal parts of length 30 cm and to each part she tied 2 white balls. After that, she cut the second ribbon into equal parts of length 35 cm and to each part she tied 3 blue balls. When she finished tying, she counted that there were 12 more blue balls than white balls. How many balls were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
30 cm |
35 cm |
|
|
Number of balloons tied to each part |
2 white balloons |
3 blue balloons |
|
|
LCM |
210 cm |
210 cm |
|
|
Number of equal parts |
210 ÷ 30 = 7 |
210 ÷ 35 = 6 |
|
|
Number of balloons for each ribbon per set |
7 x 2 = 14 |
3 x 6 = 18 |
18 - 14 = 4 |
14 + 18 = 32 |
LCM of 30 and 35 = 210
Number of sets of 2 white balls in a length of 210 cm
= 210 ÷ 30
= 7
Number of white balls in a length of 210 cm
= 7 x 2
= 14
Number of sets of 3 blue balls in a length of 210 cm
= 210 ÷ 35
= 6
Number of blue balls in a length of 210 cm
= 6 x 3
= 18
Extra number of blue balls in a length of 210 cm
= 18 - 14
= 4
Number of sets of balls
= 12 ÷ 4
= 3
Total number of balls in one set of 210 cm of white balloons and one set of 210 cm of blue balloons
= 14 + 18
= 32
Total number of balls of the two ribbons
= 3 x 32
= 96
Answer(s): 96