Vincent has 6 more 20-cent coins than 10-cent coins. After he used 8 of his 20-cent coins, the total value of 20-cent coins is $4.70 more than the total value of 10-cent coins. How many coins did he have at first?
|
20¢ |
10¢ |
Before |
1 u + 6 |
1 u |
Change |
- 8 |
|
After |
1 u - 2 |
1 u |
|
20¢ |
10¢ |
Number |
1 u - 2 |
1 u |
Value |
20 |
10 |
Total value |
20 u - 40 |
10 u |
$1 = 100¢
$4.70 = 470¢
Number of 20¢ coins in the end
= 1 u + 6 - 8
= 1 u - 2
Total value of 20¢ coins in the end
= 20 x (1 u - 2)
= 20 u - 40
Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u
After using 8 20-cent coins, the value of 20-cent coins is 470¢ more than the value of 10-cent coins. If another 470¢ is added to the 10-cent coins, the total value of 20-cent coins and 10-cent coins will be the same.
20 u - 40 = 10 u + 470
20 u - 10 u = 470 + 40
10 u = 510
1 u = 510 ÷ 10 = 51
Number of coins that Vincent had at first
= 1 u + 1 u + 6
= 2 u + 6
= (2 x 51) + 6
= 102 + 6
= 108
Answer(s): 108