In January, Jen and Tim had beads in the ratio 6 : 5. In February, each of them gave away the same number of beads. Jen then had thrice as many beads as Tim.
- Find the ratio of the number of beads Tim had in January to the number of beads he had in February.
- Find the ratio of the total number of beads both had in January to the total number of beads both had in February.
| |
Jen |
Tim |
Difference |
| Before |
6x2 =
12 u |
5x2 =
10 u |
1x2 =
2 u |
| Change |
- 9 u |
- 9 u |
|
| After |
3x1 =
3 u |
1x1 =
1 u |
2x1 =
2 u |
(a)
Since Jen and Tim gave away the same number of beads, the difference in the number of beads between Jen and Tim at first and in the end remains the same.
Make the difference in the number of beads at first and in the end the same. LCM of 1 and 2 is 2.
Tim's beads in January : Tim's beads in February
10 : 1
(b)
Total number of beads in January
= 12 u + 10 u
= 22 u
Total number of beads in February
= 3 u + 1 u
= 4 u
Total beads in January : Total beads in February
22 : 4
(÷2)11 : 2
Answer(s): (a) 10 : 1; (b) 11 : 2
