Hazel and Mark collect beads and pens. Mark has 45 less beads than pens. Mark has 3 times the number of beads Hazel has, and Hazel has 40% more pens than Mark. After Hazel gives Mark all of her beads and Mark gives Hazel 60% of his pens, Mark has 10 more beads than pens. Find the number of pens Hazel has at first.
| Hazel |
Mark |
| Pens |
Beads |
Pens |
Beads |
| 4.2 u + 63 |
1 u |
3 u + 45 |
3 u |
| + 1.8 u + 27 |
- 1 u |
- 1.8 u - 27 |
+ 1 u |
| 6 u + 90 |
0 |
1.2 u + 18 |
4 u |
100%+ 40% = 140%
140% x 3 u
=
140100 x 3 u
= 4.2 u
140% x 45
=
140100 x 45
= 63
60% x 3 u
=
60100 x 3 u
= 1.8 u
60% x 45
=
60100 x 45
= 27
If another 10 pens are given to Mark, he will have equal number of pens and beads in the end.
4 u = 1.2 u + 18 + 10
4 u - 1.2 u = 28
2.8 u = 28
1 u = 28 ÷ 2.8 = 10
Number of pens that Hazel has at first
= 4.2 u + 63
= 4.2 x 10 + 63
= 42 + 63
= 105
Answer(s): 105 
