Tiffany and Fanny had 858 beads altogether. They decided to play a game. In the first round, Fanny lost 60 beads to Tiffany. In the second round, Tiffany lost 32 beads to Fanny. At the end of the two rounds, Fanny had twice as many beads as Tiffany.
- How many beads did Tiffany have in the end?
- How many beads did Fanny have at the beginning of the game?
|
Tiffany |
Fanny |
Total |
Before |
1 u + 32 - 60 |
2 u - 32 + 60 |
858 |
Round 1 |
+ 60 |
- 60 |
|
Round 2 |
- 32 |
+ 32 |
|
After |
1 u |
2 u |
858 |
(a)
Total number of beads
= 1 u + 2 u
= 3 u
3 u = 858
1 u = 858 ÷ 3 = 286
Number of beads that Tiffany had in the end
= 1 u
= 286
(b)
Working backwards.
Number of beads that Fanny had at the end of round 2
= 2 u
= 2 x 286
= 572
Number of beads that Fanny had at the end of round 1
= 572 - 32
= 540
Number of beads that Fanny had at the beginning of the game
= 540 + 60
= 600
Answer(s): (a) 286; (b) 600