PSLEBetty 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 gold heart cutouts. After that, she cut the second ribbon into equal parts of length 35 cm and to each part she tied 5 purple heart cutouts. When she finished tying, she counted that there were 36 more purple heart cutouts than gold heart cutouts. How many heart cutouts 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 gold balloons |
5 purple 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 |
5 x 6 = 30 |
30 - 21 = 9 |
21 + 30 = 51 |
LCM of 30 and 35 = 210
Number of sets of 3 gold heart cutouts in a length of 210 cm
= 210 ÷ 30
= 7
Number of gold heart cutouts in a length of 210 cm
= 7 x 3
= 21
Number of sets of 5 purple heart cutouts in a length of 210 cm
= 210 ÷ 35
= 6
Number of purple heart cutouts in a length of 210 cm
= 6 x 5
= 30
Extra number of purple heart cutouts in a length of 210 cm
= 30 - 21
= 9
Number of sets of heart cutouts
= 36 ÷ 9
= 4
Total number of heart cutouts in one set of 210 cm of gold balloons and one set of 210 cm of purple balloons
= 21 + 30
= 51
Total number of heart cutouts of the two ribbons
= 4 x 51
= 204
Answer(s): 204