PSLELynn had two strings of the same length. She cut the first string into equal parts of length 25 cm and to each part she tied 3 pink balloons. After that, she cut the second string into equal parts of length 30 cm and to each part she tied 5 silver balloons. When she finished tying, she counted that there were 21 more silver balloons than pink balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
25 cm |
30 cm |
|
|
Number of balloons tied to each part |
3 pink balloons |
5 silver balloons |
|
|
LCM |
150 cm |
150 cm |
|
|
Number of equal parts |
150 ÷ 25 = 6 |
150 ÷ 30 = 5 |
|
|
Number of balloons for each string per set |
6 x 3 = 18 |
5 x 5 = 25 |
25 - 18 = 7 |
18 + 25 = 43 |
LCM of 25 and 30 = 150
Number of sets of 3 pink balloons in a length of 150 cm
= 150 ÷ 25
= 6
Number of pink balloons in a length of 150 cm
= 6 x 3
= 18
Number of sets of 5 silver balloons in a length of 150 cm
= 150 ÷ 30
= 5
Number of silver balloons in a length of 150 cm
= 5 x 5
= 25
Extra number of silver balloons in a length of 150 cm
= 25 - 18
= 7
Number of sets of balloons
= 21 ÷ 7
= 3
Total number of balloons in one set of 150 cm of pink balloons and one set of 150 cm of silver balloons
= 18 + 25
= 43
Total number of balloons of the two strings
= 3 x 43
= 129
Answer(s): 129