In February, Pamela and Oscar had buttons in the ratio 5 : 2. In March, each of them gave away the same number of buttons. Pamela then had five times as many buttons as Oscar.
- Find the ratio of the number of buttons Oscar had in February to the number of buttons he had in March.
- Find the ratio of the total number of buttons both had in February to the total number of buttons both had in March.
|
Pamela |
Oscar |
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 Pamela and Oscar gave away the same number of buttons, the difference in the number of buttons between Pamela and Oscar at first and in the end remains the same.
Make the difference in the number of buttons at first and in the end the same. LCM of 3 and 4 is 12.
Oscar's buttons in February : Oscar's buttons in March
8 : 3
(b)
Total number of buttons in February
= 20 u + 8 u
= 28 u
Total number of buttons in March
= 15 u + 3 u
= 18 u
Total buttons in February : Total buttons in March
28 : 18
(÷2)14 : 9
Answer(s): (a) 8 : 3; (b) 14 : 9