Yoko had some brown marbles and yellow marbles in 2 boxes. In Box D, the ratio of the number of brown marbles to yellow marbles was 8 : 5. In Box E, the number of brown marbles was 2 times the number of yellow marbles. Yoko transferred
25 of the yellow marbles from Box D to Box E. The number of marbles in Box D became 165 and the ratio of the number of brown marbles to yellow marbles in Box E became 4 : 5.
- How many yellow marbles were transferred from Box D to Box E?
- What was the number of marbles in Box E after the transfer?
|
Box D |
Box E |
|
Brown |
Yellow |
Brown |
Yellow |
Comparing brown marbles and yellow marbles at first |
8 u |
5 u |
2x2 = 4 p |
1x2 = 2 p |
Before |
|
5 u |
|
|
Change |
|
- 2 u |
|
+ 2 u |
After |
|
3 u |
|
|
Comparing brown marbles and yellow marbles in the end |
8 u |
3 u |
4 p |
5 p |
(a)
Total number of marbles in the end for Box D
= 8 u + 3 u
= 11 u
11 u = 165
1 u = 165 ÷ 11 = 15
Number of yellow marbles that were transferred from Box D to Box E
= 2 u
= 2 x 15
= 30
(b)
The number of brown marbles in Box E remains unchanged. Make the number of brown marbles in Box E the same. LCM of 2 and 4 is 4.
Increase in the number of yellow marbles in Box E
= 5 p - 2 p
= 3 p
3 p = 2 u
3 p = 30
1 p = 30 ÷ 3 = 10
Number of marbles in Box E in the end
= 4 p + 5 p
= 9 p
= 9 x 10
= 90
Answer(s): (a) 30; (b) 90