PSLEZara had two strings of the same length. She cut the first string into equal parts of length 50 cm and to each part she tied 2 black heart cutouts. After that, she cut the second string into equal parts of length 70 cm and to each part she tied 5 yellow heart cutouts. When she finished tying, she counted that there were 55 more yellow heart cutouts than black heart cutouts. How many heart cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
50 cm |
70 cm |
|
|
Number of balloons tied to each part |
2 black balloons |
5 yellow balloons |
|
|
LCM |
350 cm |
350 cm |
|
|
Number of equal parts |
350 ÷ 50 = 7 |
350 ÷ 70 = 5 |
|
|
Number of balloons for each string 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 black heart cutouts in a length of 350 cm
= 350 ÷ 50
= 7
Number of black heart cutouts in a length of 350 cm
= 7 x 2
= 14
Number of sets of 5 yellow heart cutouts in a length of 350 cm
= 350 ÷ 70
= 5
Number of yellow heart cutouts in a length of 350 cm
= 5 x 5
= 25
Extra number of yellow heart cutouts in a length of 350 cm
= 25 - 14
= 11
Number of sets of heart cutouts
= 55 ÷ 11
= 5
Total number of heart cutouts in one set of 350 cm of black balloons and one set of 350 cm of yellow balloons
= 14 + 25
= 39
Total number of heart cutouts of the two strings
= 5 x 39
= 195
Answer(s): 195