PSLEXandra 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 2 brown balloons. After that, she cut the second string into equal parts of length 35 cm and to each part she tied 5 black balloons. When she finished tying, she counted that there were 55 more black balloons than brown balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
25 cm |
35 cm |
|
|
Number of balloons tied to each part |
2 brown balloons |
5 black balloons |
|
|
LCM |
175 cm |
175 cm |
|
|
Number of equal parts |
175 ÷ 25 = 7 |
175 ÷ 35 = 5 |
|
|
Number of balloons for each string per set |
7 x 2 = 14 |
5 x 5 = 25 |
25 - 14 = 11 |
14 + 25 = 39 |
LCM of 25 and 35 = 175
Number of sets of 2 brown balloons in a length of 175 cm
= 175 ÷ 25
= 7
Number of brown balloons in a length of 175 cm
= 7 x 2
= 14
Number of sets of 5 black balloons in a length of 175 cm
= 175 ÷ 35
= 5
Number of black balloons in a length of 175 cm
= 5 x 5
= 25
Extra number of black balloons in a length of 175 cm
= 25 - 14
= 11
Number of sets of balloons
= 55 ÷ 11
= 5
Total number of balloons in one set of 175 cm of brown balloons and one set of 175 cm of black balloons
= 14 + 25
= 39
Total number of balloons of the two strings
= 5 x 39
= 195
Answer(s): 195