PSLEOlivium had two strings of the same length. She cut the first string into equal parts of length 70 cm and to each part she tied 2 blue heart cutouts. After that, she cut the second string into equal parts of length 90 cm and to each part she tied 3 grey heart cutouts. When she finished tying, she counted that there were 15 more grey heart cutouts than blue heart cutouts. How many heart cutouts were there altogether?
|
First string |
Second string |
Difference |
Total |
Length of each part |
70 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 blue balloons |
3 grey balloons |
|
|
LCM |
630 cm |
630 cm |
|
|
Number of equal parts |
630 ÷ 70 = 9 |
630 ÷ 90 = 7 |
|
|
Number of balloons for each string per set |
9 x 2 = 18 |
3 x 7 = 21 |
21 - 18 = 3 |
18 + 21 = 39 |
LCM of 70 and 90 = 630
Number of sets of 2 blue heart cutouts in a length of 630 cm
= 630 ÷ 70
= 9
Number of blue heart cutouts in a length of 630 cm
= 9 x 2
= 18
Number of sets of 3 grey heart cutouts in a length of 630 cm
= 630 ÷ 90
= 7
Number of grey heart cutouts in a length of 630 cm
= 7 x 3
= 21
Extra number of grey heart cutouts in a length of 630 cm
= 21 - 18
= 3
Number of sets of heart cutouts
= 15 ÷ 3
= 5
Total number of heart cutouts in one set of 630 cm of blue balloons and one set of 630 cm of grey balloons
= 18 + 21
= 39
Total number of heart cutouts of the two strings
= 5 x 39
= 195
Answer(s): 195