PSLESabrina had two strings of the same length. She cut the first string into equal parts of length 35 cm and to each part she tied 2 black balloons. After that, she cut the second string into equal parts of length 50 cm and to each part she tied 5 blue balloons. When she finished tying, she counted that there were 45 more blue balloons than black balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
35 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 black balloons |
5 blue balloons |
|
|
LCM |
350 cm |
350 cm |
|
|
Number of equal parts |
350 ÷ 35 = 10 |
350 ÷ 50 = 7 |
|
|
Number of balloons for each string per set |
10 x 2 = 20 |
5 x 7 = 35 |
35 - 20 = 15 |
20 + 35 = 55 |
LCM of 35 and 50 = 350
Number of sets of 2 black balloons in a length of 350 cm
= 350 ÷ 35
= 10
Number of black balloons in a length of 350 cm
= 10 x 2
= 20
Number of sets of 5 blue balloons in a length of 350 cm
= 350 ÷ 50
= 7
Number of blue balloons in a length of 350 cm
= 7 x 5
= 35
Extra number of blue balloons in a length of 350 cm
= 35 - 20
= 15
Number of sets of balloons
= 45 ÷ 15
= 3
Total number of balloons in one set of 350 cm of black balloons and one set of 350 cm of blue balloons
= 20 + 35
= 55
Total number of balloons of the two strings
= 3 x 55
= 165
Answer(s): 165