PSLEJulie had two ribbons of the same length. She cut the first ribbon into equal parts of length 80 cm and to each part she tied 3 brown heart cutouts. After that, she cut the second ribbon into equal parts of length 90 cm and to each part she tied 4 green heart cutouts. When she finished tying, she counted that there were 10 more green heart cutouts than brown heart cutouts. How many heart cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
80 cm |
90 cm |
|
|
Number of balloons tied to each part |
3 brown balloons |
4 green balloons |
|
|
LCM |
720 cm |
720 cm |
|
|
Number of equal parts |
720 ÷ 80 = 9 |
720 ÷ 90 = 8 |
|
|
Number of balloons for each ribbon per set |
9 x 3 = 27 |
4 x 8 = 32 |
32 - 27 = 5 |
27 + 32 = 59 |
LCM of 80 and 90 = 720
Number of sets of 3 brown heart cutouts in a length of 720 cm
= 720 ÷ 80
= 9
Number of brown heart cutouts in a length of 720 cm
= 9 x 3
= 27
Number of sets of 4 green heart cutouts in a length of 720 cm
= 720 ÷ 90
= 8
Number of green heart cutouts in a length of 720 cm
= 8 x 4
= 32
Extra number of green heart cutouts in a length of 720 cm
= 32 - 27
= 5
Number of sets of heart cutouts
= 10 ÷ 5
= 2
Total number of heart cutouts in one set of 720 cm of brown balloons and one set of 720 cm of green balloons
= 27 + 32
= 59
Total number of heart cutouts of the two ribbons
= 2 x 59
= 118
Answer(s): 118