In January, Opal and Neave had marbles in the ratio 5 : 2. In February, each of them gave away the same number of marbles. Opal then had five times as many marbles as Neave.
- Find the ratio of the number of marbles Neave had in January to the number of marbles he had in February.
- Find the ratio of the total number of marbles both had in January to the total number of marbles both had in February.
| |
Opal |
Neave |
Difference |
| Before |
5x4 =
20 u |
2x4 =
8 u |
3x4 =
12 u |
| Change |
- 5 u |
- 5 u |
|
| After |
5x3 =
15 u |
1x3 =
3 u |
4x3 =
12 u |
(a)
Since Opal and Neave gave away the same number of marbles, the difference in the number of marbles between Opal 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 3 and 4 is 12.
Neave's marbles in January : Neave's marbles in February
8 : 3
(b)
Total number of marbles in January
= 20 u + 8 u
= 28 u
Total number of marbles in February
= 15 u + 3 u
= 18 u
Total marbles in January : Total marbles in February
28 : 18
(÷2)14 : 9
Answer(s): (a) 8 : 3; (b) 14 : 9
