PSLETina had two strings of the same length. She cut the first string into equal parts of length 20 cm and to each part she tied 2 gold balloons. After that, she cut the second string into equal parts of length 35 cm and to each part she tied 5 silver balloons. When she finished tying, she counted that there were 30 more silver balloons than gold balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
20 cm |
35 cm |
|
|
Number of balloons tied to each part |
2 gold balloons |
5 silver balloons |
|
|
LCM |
140 cm |
140 cm |
|
|
Number of equal parts |
140 ÷ 20 = 7 |
140 ÷ 35 = 4 |
|
|
Number of balloons for each string per set |
7 x 2 = 14 |
5 x 4 = 20 |
20 - 14 = 6 |
14 + 20 = 34 |
LCM of 20 and 35 = 140
Number of sets of 2 gold balloons in a length of 140 cm
= 140 ÷ 20
= 7
Number of gold balloons in a length of 140 cm
= 7 x 2
= 14
Number of sets of 5 silver balloons in a length of 140 cm
= 140 ÷ 35
= 4
Number of silver balloons in a length of 140 cm
= 4 x 5
= 20
Extra number of silver balloons in a length of 140 cm
= 20 - 14
= 6
Number of sets of balloons
= 30 ÷ 6
= 5
Total number of balloons in one set of 140 cm of gold balloons and one set of 140 cm of silver balloons
= 14 + 20
= 34
Total number of balloons of the two strings
= 5 x 34
= 170
Answer(s): 170