PSLEDana had two ribbons of the same length. She cut the first ribbon into equal parts of length 30 cm and to each part she tied 4 white cartoon cutouts. After that, she cut the second ribbon into equal parts of length 35 cm and to each part she tied 5 black cartoon cutouts. When she finished tying, she counted that there were 6 more black cartoon cutouts than white cartoon cutouts. How many cartoon cutouts were there altogether?
|
First ribbon |
Second ribbon |
Difference |
Total |
Length of each part |
30 cm |
35 cm |
|
|
Number of balloons tied to each part |
4 white balloons |
5 black balloons |
|
|
LCM |
210 cm |
210 cm |
|
|
Number of equal parts |
210 ÷ 30 = 7 |
210 ÷ 35 = 6 |
|
|
Number of balloons for each ribbon per set |
7 x 4 = 28 |
5 x 6 = 30 |
30 - 28 = 2 |
28 + 30 = 58 |
LCM of 30 and 35 = 210
Number of sets of 4 white cartoon cutouts in a length of 210 cm
= 210 ÷ 30
= 7
Number of white cartoon cutouts in a length of 210 cm
= 7 x 4
= 28
Number of sets of 5 black cartoon cutouts in a length of 210 cm
= 210 ÷ 35
= 6
Number of black cartoon cutouts in a length of 210 cm
= 6 x 5
= 30
Extra number of black cartoon cutouts in a length of 210 cm
= 30 - 28
= 2
Number of sets of cartoon cutouts
= 6 ÷ 2
= 3
Total number of cartoon cutouts in one set of 210 cm of white balloons and one set of 210 cm of black balloons
= 28 + 30
= 58
Total number of cartoon cutouts of the two ribbons
= 3 x 58
= 174
Answer(s): 174