PSLENatalie had two strings of the same length. She cut the first string into equal parts of length 40 cm and to each part she tied 3 black flags. After that, she cut the second string into equal parts of length 45 cm and to each part she tied 5 purple flags. When she finished tying, she counted that there were 26 more purple flags than black flags. How many flags were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
40 cm |
45 cm |
|
|
Number of balloons tied to each part |
3 black balloons |
5 purple balloons |
|
|
LCM |
360 cm |
360 cm |
|
|
Number of equal parts |
360 ÷ 40 = 9 |
360 ÷ 45 = 8 |
|
|
Number of balloons for each string per set |
9 x 3 = 27 |
5 x 8 = 40 |
40 - 27 = 13 |
27 + 40 = 67 |
LCM of 40 and 45 = 360
Number of sets of 3 black flags in a length of 360 cm
= 360 ÷ 40
= 9
Number of black flags in a length of 360 cm
= 9 x 3
= 27
Number of sets of 5 purple flags in a length of 360 cm
= 360 ÷ 45
= 8
Number of purple flags in a length of 360 cm
= 8 x 5
= 40
Extra number of purple flags in a length of 360 cm
= 40 - 27
= 13
Number of sets of flags
= 26 ÷ 13
= 2
Total number of flags in one set of 360 cm of black balloons and one set of 360 cm of purple balloons
= 27 + 40
= 67
Total number of flags of the two strings
= 2 x 67
= 134
Answer(s): 134