PSLEWendy had two ribbons of the same length. She cut the first ribbon into equal parts of length 70 cm and to each part she tied 2 red cartoon cutouts. After that, she cut the second ribbon into equal parts of length 90 cm and to each part she tied 4 gold cartoon cutouts. When she finished tying, she counted that there were 20 more gold cartoon cutouts than red cartoon cutouts. How many cartoon cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
70 cm |
90 cm |
|
|
Number of balloons tied to each part |
2 red balloons |
4 gold balloons |
|
|
LCM |
630 cm |
630 cm |
|
|
Number of equal parts |
630 ÷ 70 = 9 |
630 ÷ 90 = 7 |
|
|
Number of balloons for each ribbon per set |
9 x 2 = 18 |
4 x 7 = 28 |
28 - 18 = 10 |
18 + 28 = 46 |
LCM of 70 and 90 = 630
Number of sets of 2 red cartoon cutouts in a length of 630 cm
= 630 ÷ 70
= 9
Number of red cartoon cutouts in a length of 630 cm
= 9 x 2
= 18
Number of sets of 4 gold cartoon cutouts in a length of 630 cm
= 630 ÷ 90
= 7
Number of gold cartoon cutouts in a length of 630 cm
= 7 x 4
= 28
Extra number of gold cartoon cutouts in a length of 630 cm
= 28 - 18
= 10
Number of sets of cartoon cutouts
= 20 ÷ 10
= 2
Total number of cartoon cutouts in one set of 630 cm of red balloons and one set of 630 cm of gold balloons
= 18 + 28
= 46
Total number of cartoon cutouts of the two ribbons
= 2 x 46
= 92
Answer(s): 92