In April, Sarah and Julian had marbles in the ratio 10 : 7. In May, each of them gave away the same number of marbles. Sarah then had thrice as many marbles as Julian.
- Find the ratio of the number of marbles Julian had in April to the number of marbles he had in May.
- Find the ratio of the total number of marbles both had in April to the total number of marbles both had in May.
| |
Sarah |
Julian |
Difference |
| Before |
10x2 =
20 u |
7x2 =
14 u |
3x2 =
6 u |
| Change |
- 11 u |
- 11 u |
|
| After |
3x3 =
9 u |
1x3 =
3 u |
2x3 =
6 u |
(a)
Since Sarah and Julian gave away the same number of marbles, the difference in the number of marbles between Sarah and Julian 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 2 is 6.
Julian's marbles in April : Julian's marbles in May
14 : 3
(b)
Total number of marbles in April
= 20 u + 14 u
= 34 u
Total number of marbles in May
= 9 u + 3 u
= 12 u
Total marbles in April : Total marbles in May
34 : 12
(÷2)17 : 6
Answer(s): (a) 14 : 3; (b) 17 : 6
