Roshel and Jenson collect beads and cards. Jenson has 68 less beads than cards. Jenson has 5 times the number of beads Roshel has, and Roshel has 25% more cards than Jenson. After Roshel gives Jenson all of her beads and Jenson gives Roshel 75% of his cards, Jenson has 21 more beads than cards. Find the number of cards Roshel has at first.
Roshel |
Jenson |
Cards |
Beads |
Cards |
Beads |
6.25 u + 85 |
1 u |
5 u + 68 |
5 u |
+ 3.75 u + 51 |
- 1 u |
- 3.75 u - 51 |
+ 1 u |
10 u + 136 |
0 |
1.25 u + 17 |
6 u |
100%+ 25% = 125%
125% x 5 u
=
125100 x 5 u
= 6.25 u
125% x 68
=
125100 x 68
= 85
75% x 5 u
=
75100 x 5 u
= 3.75 u
75% x 68
=
75100 x 68
= 51
If another 21 cards are given to Jenson, he will have equal number of cards and beads in the end.
6 u = 1.25 u + 17 + 21
6 u - 1.25 u = 38
4.75 u = 38
1 u = 38 ÷ 4.75 = 8
Number of cards that Roshel has at first
= 6.25 u + 85
= 6.25 x 8 + 85
= 50 + 85
= 135
Answer(s): 135