PSLEXylium had two strings of the same length. She cut the first string into equal parts of length 80 cm and to each part she tied 3 gold heart cutouts. After that, she cut the second string into equal parts of length 90 cm and to each part she tied 5 yellow heart cutouts. When she finished tying, she counted that there were 65 more yellow heart cutouts than gold heart cutouts. How many heart cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
80 cm |
90 cm |
|
|
Number of balloons tied to each part |
3 gold balloons |
5 yellow balloons |
|
|
LCM |
720 cm |
720 cm |
|
|
Number of equal parts |
720 ÷ 80 = 9 |
720 ÷ 90 = 8 |
|
|
Number of balloons for each string per set |
9 x 3 = 27 |
5 x 8 = 40 |
40 - 27 = 13 |
27 + 40 = 67 |
LCM of 80 and 90 = 720
Number of sets of 3 gold heart cutouts in a length of 720 cm
= 720 ÷ 80
= 9
Number of gold heart cutouts in a length of 720 cm
= 9 x 3
= 27
Number of sets of 5 yellow heart cutouts in a length of 720 cm
= 720 ÷ 90
= 8
Number of yellow heart cutouts in a length of 720 cm
= 8 x 5
= 40
Extra number of yellow heart cutouts in a length of 720 cm
= 40 - 27
= 13
Number of sets of heart cutouts
= 65 ÷ 13
= 5
Total number of heart cutouts in one set of 720 cm of gold balloons and one set of 720 cm of yellow balloons
= 27 + 40
= 67
Total number of heart cutouts of the two strings
= 5 x 67
= 335
Answer(s): 335