Usha and Vincent collect pencils and coins. Vincent has 100 less pencils than coins. Vincent has 5 times the number of pencils Usha has, and Usha has 30% more coins than Vincent. After Usha gives Vincent all of her pencils and Vincent gives Usha 70% of his coins, Vincent has 6 more pencils than coins. Find the number of coins Usha has at first.
Usha |
Vincent |
Coins |
Pencils |
Coins |
Pencils |
6.5 u + 130 |
1 u |
5 u + 100 |
5 u |
+ 3.5 u + 70 |
- 1 u |
- 3.5 u - 70 |
+ 1 u |
10 u + 200 |
0 |
1.5 u + 30 |
6 u |
100%+ 30% = 130%
130% x 5 u
=
130100 x 5 u
= 6.5 u
130% x 100
=
130100 x 100
= 130
70% x 5 u
=
70100 x 5 u
= 3.5 u
70% x 100
=
70100 x 100
= 70
If another 6 coins are given to Vincent, he will have equal number of coins and pencils in the end.
6 u = 1.5 u + 30 + 6
6 u - 1.5 u = 36
4.5 u = 36
1 u = 36 ÷ 4.5 = 8
Number of coins that Usha has at first
= 6.5 u + 130
= 6.5 x 8 + 130
= 52 + 130
= 182
Answer(s): 182