PSLEDiana 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 40 cm and to each part she tied 5 brown stars. When she finished tying, she counted that there were 9 more brown stars than green stars. How many stars were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
30 cm |
40 cm |
|
|
Number of balloons tied to each part |
3 green balloons |
5 brown balloons |
|
|
LCM |
120 cm |
120 cm |
|
|
Number of equal parts |
120 ÷ 30 = 4 |
120 ÷ 40 = 3 |
|
|
Number of balloons for each ribbon per set |
4 x 3 = 12 |
5 x 3 = 15 |
15 - 12 = 3 |
12 + 15 = 27 |
LCM of 30 and 40 = 120
Number of sets of 3 green stars in a length of 120 cm
= 120 ÷ 30
= 4
Number of green stars in a length of 120 cm
= 4 x 3
= 12
Number of sets of 5 brown stars in a length of 120 cm
= 120 ÷ 40
= 3
Number of brown stars in a length of 120 cm
= 3 x 5
= 15
Extra number of brown stars in a length of 120 cm
= 15 - 12
= 3
Number of sets of stars
= 9 ÷ 3
= 3
Total number of stars in one set of 120 cm of green balloons and one set of 120 cm of brown balloons
= 12 + 15
= 27
Total number of stars of the two ribbons
= 3 x 27
= 81
Answer(s): 81