PSLEPenelope had two ribbons of the same length. She cut the first ribbon into equal parts of length 30 cm and to each part she tied 3 green stars. After that, she cut the second ribbon into equal parts of length 35 cm and to each part she tied 4 black stars. When she finished tying, she counted that there were 12 more black stars than green stars. How many stars were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
30 cm |
35 cm |
|
|
Number of balloons tied to each part |
3 green balloons |
4 black balloons |
|
|
LCM |
210 cm |
210 cm |
|
|
Number of equal parts |
210 ÷ 30 = 7 |
210 ÷ 35 = 6 |
|
|
Number of balloons for each ribbon per set |
7 x 3 = 21 |
4 x 6 = 24 |
24 - 21 = 3 |
21 + 24 = 45 |
LCM of 30 and 35 = 210
Number of sets of 3 green stars in a length of 210 cm
= 210 ÷ 30
= 7
Number of green stars in a length of 210 cm
= 7 x 3
= 21
Number of sets of 4 black stars in a length of 210 cm
= 210 ÷ 35
= 6
Number of black stars in a length of 210 cm
= 6 x 4
= 24
Extra number of black stars in a length of 210 cm
= 24 - 21
= 3
Number of sets of stars
= 12 ÷ 3
= 4
Total number of stars in one set of 210 cm of green balloons and one set of 210 cm of black balloons
= 21 + 24
= 45
Total number of stars of the two ribbons
= 4 x 45
= 180
Answer(s): 180