Jen and Sam collect stickers and cards. Sam has 40 more cards than stickers. Sam has 4 times the number of stickers Jen has, and Jen has 20% more cards than Sam. After Jen gives Sam all of her stickers and Sam gives Jen 70% of his cards, Sam has 7 more stickers than cards. Find the number of cards Jen has at first.
| Jen |
Sam |
| Cards |
Stickers |
Cards |
Stickers |
| 4.8 u + 48 |
1 u |
4 u + 40 |
4 u |
| + 2.8 u + 28 |
- 1 u |
- 2.8 u - 28 |
+ 1 u |
| 7.6 u + 76 |
0 |
1.2 u + 12 |
5 u |
100% + 20% = 120%
120% x 4 u
=
120100 x 4 u
= 4.8 u
120% x 40
=
120100 x 40
= 48
70% x 4 u
=
70100 x 4 u
= 2.8 u
70% x 40
=
70100 x 40
= 28
If another 7 cards are given to Sam, he will have equal number of cards and stickers in the end.
5 u = 1.2 u + 12 + 7
5 u - 1.2 u = 19
3.8 u = 19
1 u = 19 ÷ 3.8 = 5
Number of cards that Jen has at first
= 4.8 u + 48
= 4.8 x 5 + 48
= 24 + 48
= 72
Answer(s): 72 
