PSLEPenelope had two ribbons of the same length. She cut the first ribbon into equal parts of length 40 cm and to each part she tied 2 gold heart cutouts. After that, she cut the second ribbon into equal parts of length 50 cm and to each part she tied 3 pink heart cutouts. When she finished tying, she counted that there were 8 more pink heart cutouts than gold heart cutouts. How many heart cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
40 cm |
50 cm |
|
|
Number of balloons tied to each part |
2 gold balloons |
3 pink balloons |
|
|
LCM |
200 cm |
200 cm |
|
|
Number of equal parts |
200 ÷ 40 = 5 |
200 ÷ 50 = 4 |
|
|
Number of balloons for each ribbon per set |
5 x 2 = 10 |
3 x 4 = 12 |
12 - 10 = 2 |
10 + 12 = 22 |
LCM of 40 and 50 = 200
Number of sets of 2 gold heart cutouts in a length of 200 cm
= 200 ÷ 40
= 5
Number of gold heart cutouts in a length of 200 cm
= 5 x 2
= 10
Number of sets of 3 pink heart cutouts in a length of 200 cm
= 200 ÷ 50
= 4
Number of pink heart cutouts in a length of 200 cm
= 4 x 3
= 12
Extra number of pink heart cutouts in a length of 200 cm
= 12 - 10
= 2
Number of sets of heart cutouts
= 8 ÷ 2
= 4
Total number of heart cutouts in one set of 200 cm of gold balloons and one set of 200 cm of pink balloons
= 10 + 12
= 22
Total number of heart cutouts of the two ribbons
= 4 x 22
= 88
Answer(s): 88