Nora and Tom collect pens and beads. Tom has 40 less pens than beads. Tom has 2 times the number of pens Nora has, and Nora has 25% more beads than Tom. After Nora gives Tom all of her pens and Tom gives Nora 75% of his beads, Tom has 10 less beads than pens. Find the number of beads Nora has at first.
| Nora |
Tom |
| Beads |
Pens |
Beads |
Pens |
| 2.5 u + 50 |
1 u |
2 u + 40 |
2 u |
| + 1.5 u + 30 |
- 1 u |
- 1.5 u - 30 |
+ 1 u |
| 4 u + 80 |
0 |
0.5 u + 10 |
3 u |
100%+ 25% = 125%
125% x 2 u
=
125100 x 2 u
= 2.5 u
125% x 40
=
125100 x 40
= 50
75% x 2 u
=
75100 x 2 u
= 1.5 u
75% x 40
=
75100 x 40
= 30
If another 10 beads are given to Tom, he will have equal number of beads and pens in the end.
3 u = 0.5 u + 10 + 10
3 u - 0.5 u = 20
2.5 u = 20
1 u = 20 ÷ 2.5 = 8
Number of beads that Nora has at first
= 2.5 u + 50
= 2.5 x 8 + 50
= 20 + 50
= 70
Answer(s): 70 
