PSLEWinnie 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 grey stars. After that, she cut the second ribbon into equal parts of length 90 cm and to each part she tied 3 red stars. When she finished tying, she counted that there were 12 more red stars than grey stars. How many stars 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 grey balloons |
3 red 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 grey stars in a length of 630 cm
= 630 ÷ 70
= 9
Number of grey stars in a length of 630 cm
= 9 x 2
= 18
Number of sets of 3 red stars in a length of 630 cm
= 630 ÷ 90
= 7
Number of red stars in a length of 630 cm
= 7 x 3
= 21
Extra number of red stars in a length of 630 cm
= 21 - 18
= 3
Number of sets of stars
= 12 ÷ 3
= 4
Total number of stars in one set of 630 cm of grey balloons and one set of 630 cm of red balloons
= 18 + 21
= 39
Total number of stars of the two ribbons
= 4 x 39
= 156
Answer(s): 156