Anna and Rael collect coins and beads. Rael has 70 more beads than coins. Rael has 2 times the number of coins Anna has, and Anna has 40% more beads than Rael. After Anna gives Rael all of her coins and Rael gives Anna 60% of his beads, Rael has 5 more coins than beads. Find the number of beads Anna has at first.
| Anna |
Rael |
| Beads |
Coins |
Beads |
Coins |
| 2.8 u + 98 |
1 u |
2 u + 70 |
2 u |
| + 1.2 u + 42 |
- 1 u |
- 1.2 u - 42 |
+ 1 u |
| 4 u + 140 |
0 |
0.8 u + 28 |
3 u |
100% + 40% = 140%
140% x 2 u
=
140100 x 2 u
= 2.8 u
140% x 70
=
140100 x 70
= 98
60% x 2 u
=
60100 x 2 u
= 1.2 u
60% x 70
=
60100 x 70
= 42
If another 5 beads are given to Rael, he will have equal number of beads and coins in the end.
3 u = 0.8 u + 28 + 5
3 u - 0.8 u = 33
2.2 u = 33
1 u = 33 ÷ 2.2 = 15
Number of beads that Anna has at first
= 2.8 u + 98
= 2.8 x 15 + 98
= 42 + 98
= 140
Answer(s): 140 
