PSLEXandra had two ribbons of the same length. She cut the first ribbon into equal parts of length 70 cm and to each part she tied 2 black flags. After that, she cut the second ribbon into equal parts of length 90 cm and to each part she tied 3 purple flags. When she finished tying, she counted that there were 9 more purple flags than black flags. How many flags were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
70 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 black balloons |
3 purple balloons |
|
|
LCM |
630 cm |
630 cm |
|
|
Number of equal parts |
630 ÷ 70 = 9 |
630 ÷ 90 = 7 |
|
|
Number of balloons for each ribbon per set |
9 x 2 = 18 |
3 x 7 = 21 |
21 - 18 = 3 |
18 + 21 = 39 |
LCM of 70 and 90 = 630
Number of sets of 2 black flags in a length of 630 cm
= 630 ÷ 70
= 9
Number of black flags in a length of 630 cm
= 9 x 2
= 18
Number of sets of 3 purple flags in a length of 630 cm
= 630 ÷ 90
= 7
Number of purple flags in a length of 630 cm
= 7 x 3
= 21
Extra number of purple flags in a length of 630 cm
= 21 - 18
= 3
Number of sets of flags
= 9 ÷ 3
= 3
Total number of flags in one set of 630 cm of black balloons and one set of 630 cm of purple balloons
= 18 + 21
= 39
Total number of flags of the two ribbons
= 3 x 39
= 117
Answer(s): 117