In February, Gwen and Neave had marbles in the ratio 5 : 3. In March, each of them gave away the same number of marbles. Gwen then had four times as many marbles as Neave.
- Find the ratio of the number of marbles Neave had in February to the number of marbles he had in March.
- Find the ratio of the total number of marbles both had in February to the total number of marbles both had in March.
| |
Gwen |
Neave |
Difference |
| Before |
5x3 =
15 u |
3x3 =
9 u |
2x3 =
6 u |
| Change |
- 7 u |
- 7 u |
|
| After |
4x2 =
8 u |
1x2 =
2 u |
3x2 =
6 u |
(a)
Since Gwen and Neave gave away the same number of marbles, the difference in the number of marbles between Gwen and Neave at first and in the end remains the same.
Make the difference in the number of marbles at first and in the end the same. LCM of 2 and 3 is 6.
Neave's marbles in February : Neave's marbles in March
9 : 2
(b)
Total number of marbles in February
= 15 u + 9 u
= 24 u
Total number of marbles in March
= 8 u + 2 u
= 10 u
Total marbles in February : Total marbles in March
24 : 10
(÷2)12 : 5
Answer(s): (a) 9 : 2; (b) 12 : 5
