PSLEPamela had two ribbons of the same length. She cut the first ribbon into equal parts of length 50 cm and to each part she tied 2 gold heart cutouts. After that, she cut the second ribbon into equal parts of length 70 cm and to each part she tied 5 blue heart cutouts. When she finished tying, she counted that there were 33 more blue heart cutouts than gold heart cutouts. How many heart cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
50 cm |
70 cm |
|
|
Number of balloons tied to each part |
2 gold balloons |
5 blue balloons |
|
|
LCM |
350 cm |
350 cm |
|
|
Number of equal parts |
350 ÷ 50 = 7 |
350 ÷ 70 = 5 |
|
|
Number of balloons for each ribbon per set |
7 x 2 = 14 |
5 x 5 = 25 |
25 - 14 = 11 |
14 + 25 = 39 |
LCM of 50 and 70 = 350
Number of sets of 2 gold heart cutouts in a length of 350 cm
= 350 ÷ 50
= 7
Number of gold heart cutouts in a length of 350 cm
= 7 x 2
= 14
Number of sets of 5 blue heart cutouts in a length of 350 cm
= 350 ÷ 70
= 5
Number of blue heart cutouts in a length of 350 cm
= 5 x 5
= 25
Extra number of blue heart cutouts in a length of 350 cm
= 25 - 14
= 11
Number of sets of heart cutouts
= 33 ÷ 11
= 3
Total number of heart cutouts in one set of 350 cm of gold balloons and one set of 350 cm of blue balloons
= 14 + 25
= 39
Total number of heart cutouts of the two ribbons
= 3 x 39
= 117
Answer(s): 117