In January, Linda and Zeph had marbles in the ratio 13 : 8. In February, each of them gave away the same number of marbles. Linda then had five times as many marbles as Zeph.
- Find the ratio of the number of marbles Zeph 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.
| |
Linda |
Zeph |
Difference |
| Before |
13x4 =
52 u |
8x4 =
32 u |
5x4 =
20 u |
| Change |
- 27 u |
- 27 u |
|
| After |
5x5 =
25 u |
1x5 =
5 u |
4x5 =
20 u |
(a)
Since Linda and Zeph gave away the same number of marbles, the difference in the number of marbles between Linda and Zeph 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 5 and 4 is 20.
Zeph's marbles in January : Zeph's marbles in February
32 : 5
(b)
Total number of marbles in January
= 52 u + 32 u
= 84 u
Total number of marbles in February
= 25 u + 5 u
= 30 u
Total marbles in January : Total marbles in February
84 : 30
(÷6)14 : 5
Answer(s): (a) 32 : 5; (b) 14 : 5
