Anna had some yellow pens and gold pens in 2 packets. In Packet A, the ratio of the number of yellow pens to gold pens was 10 : 3. In Packet B, the number of yellow pens was 2 times the number of gold pens. Anna transferred
23 of the gold pens from Packet A to Packet B. The number of pens in Packet A became 33 and the ratio of the number of yellow pens to gold pens in Packet B became 4 : 5.
- How many gold pens were transferred from Packet A to Packet B?
- What was the number of pens in Packet B after the transfer?
|
Packet A |
Packet B |
|
Yellow |
Gold |
Yellow |
Gold |
Comparing yellow pens and gold pens at first |
10 u |
3 u |
2x2 = 4 p |
1x2 = 2 p |
Before |
|
3 u |
|
|
Change |
|
- 2 u |
|
+ 2 u |
After |
|
1 u |
|
|
Comparing yellow pens and gold pens in the end |
10 u |
1 u |
4 p |
5 p |
(a)
Total number of pens in the end for Packet A
= 10 u + 1 u
= 11 u
11 u = 33
1 u = 33 ÷ 11 = 3
Number of gold pens that were transferred from Packet A to Packet B
= 2 u
= 2 x 3
= 6
(b)
The number of yellow pens in Packet B remains unchanged. Make the number of yellow pens in Packet B the same. LCM of 2 and 4 is 4.
Increase in the number of gold pens in Packet B
= 5 p - 2 p
= 3 p
3 p = 2 u
3 p = 6
1 p = 6 ÷ 3 = 2
Number of pens in Packet B in the end
= 4 p + 5 p
= 9 p
= 9 x 2
= 18
Answer(s): (a) 6; (b) 18