PSLEZoe 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 4 grey balloons. After that, she cut the second string into equal parts of length 40 cm and to each part she tied 5 pink balloons. When she finished tying, she counted that there were 15 more pink balloons than grey balloons. How many balloons were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
35 cm |
40 cm |
|
|
Number of balloons tied to each part |
4 grey balloons |
5 pink balloons |
|
|
LCM |
280 cm |
280 cm |
|
|
Number of equal parts |
280 ÷ 35 = 8 |
280 ÷ 40 = 7 |
|
|
Number of balloons for each string per set |
8 x 4 = 32 |
5 x 7 = 35 |
35 - 32 = 3 |
32 + 35 = 67 |
LCM of 35 and 40 = 280
Number of sets of 4 grey balloons in a length of 280 cm
= 280 ÷ 35
= 8
Number of grey balloons in a length of 280 cm
= 8 x 4
= 32
Number of sets of 5 pink balloons in a length of 280 cm
= 280 ÷ 40
= 7
Number of pink balloons in a length of 280 cm
= 7 x 5
= 35
Extra number of pink balloons in a length of 280 cm
= 35 - 32
= 3
Number of sets of balloons
= 15 ÷ 3
= 5
Total number of balloons in one set of 280 cm of grey balloons and one set of 280 cm of pink balloons
= 32 + 35
= 67
Total number of balloons of the two strings
= 5 x 67
= 335
Answer(s): 335