In January, Kathy and Warren had marbles in the ratio 7 : 5. In February, each of them gave away the same number of marbles. Kathy then had five times as many marbles as Warren.
- Find the ratio of the number of marbles Warren 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.
| |
Kathy |
Warren |
Difference |
| Before |
7x2 =
14 u |
5x2 =
10 u |
2x2 =
4 u |
| Change |
- 9 u |
- 9 u |
|
| After |
5x1 =
5 u |
1x1 =
1 u |
4x1 =
4 u |
(a)
Since Kathy and Warren gave away the same number of marbles, the difference in the number of marbles between Kathy and Warren 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 4 is 4.
Warren's marbles in January : Warren's marbles in February
10 : 1
(b)
Total number of marbles in January
= 14 u + 10 u
= 24 u
Total number of marbles in February
= 5 u + 1 u
= 6 u
Total marbles in January : Total marbles in February
24 : 6
(÷6)4 : 1
Answer(s): (a) 10 : 1; (b) 4 : 1
