In February, Xandra and Warren had marbles in the ratio 15 : 4. In March, each of them gave away the same number of marbles. Xandra then had five times as many marbles as Warren.
- Find the ratio of the number of marbles Warren 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.
| |
Xandra |
Warren |
Difference |
| Before |
15x4 =
60 u |
4x4 =
16 u |
11x4 =
44 u |
| Change |
- 5 u |
- 5 u |
|
| After |
5x11 =
55 u |
1x11 =
11 u |
4x11 =
44 u |
(a)
Since Xandra and Warren gave away the same number of marbles, the difference in the number of marbles between Xandra 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 11 and 4 is 44.
Warren's marbles in February : Warren's marbles in March
16 : 11
(b)
Total number of marbles in February
= 60 u + 16 u
= 76 u
Total number of marbles in March
= 55 u + 11 u
= 66 u
Total marbles in February : Total marbles in March
76 : 66
(÷2)38 : 33
Answer(s): (a) 16 : 11; (b) 38 : 33
