Opal and Sam collect erasers and pens. Sam has 100 less erasers than pens. Sam has 4 times the number of erasers Opal has, and Opal has 20% more pens than Sam. After Opal gives Sam all of her erasers and Sam gives Opal 70% of his pens, Sam has 8 more erasers than pens. Find the number of pens Opal has at first.
| Opal |
Sam |
| Pens |
Erasers |
Pens |
Erasers |
| 4.8 u + 120 |
1 u |
4 u + 100 |
4 u |
| + 2.8 u + 70 |
- 1 u |
- 2.8 u - 70 |
+ 1 u |
| 7.6 u + 190 |
0 |
1.2 u + 30 |
5 u |
100%+ 20% = 120%
120% x 4 u
=
120100 x 4 u
= 4.8 u
120% x 100
=
120100 x 100
= 120
70% x 4 u
=
70100 x 4 u
= 2.8 u
70% x 100
=
70100 x 100
= 70
If another 8 pens are given to Sam, he will have equal number of pens and erasers in the end.
5 u = 1.2 u + 30 + 8
5 u - 1.2 u = 38
3.8 u = 38
1 u = 38 ÷ 3.8 = 10
Number of pens that Opal has at first
= 4.8 u + 120
= 4.8 x 10 + 120
= 48 + 120
= 168
Answer(s): 168 
