David has 9 more 20-cent coins than 10-cent coins. After he used 10 of his 20-cent coins, the total value of 20-cent coins is $1.90 more than the total value of 10-cent coins. How many coins did he have at first?
| |
20¢ |
10¢ |
| Before |
1 u + 9 |
1 u |
| Change |
- 10 |
|
| After |
1 u - 1 |
1 u |
| |
20¢ |
10¢ |
| Number |
1 u - 1 |
1 u |
| Value |
20 |
10 |
| Total value |
20 u - 20 |
10 u |
$1 = 100¢
$1.90 = 190¢
Number of 20¢ coins in the end
= 1 u + 9 - 10
= 1 u - 1
Total value of 20¢ coins in the end
= 20 x (1 u - 1)
= 20 u - 20
Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u
After using 10 20-cent coins, the value of 20-cent coins is 190¢ more than the value of 10-cent coins. If another 190¢ is added to the 10-cent coins, the total value of 20-cent coins and 10-cent coins will be the same.
20 u - 20 = 10 u + 190
20 u - 10 u = 190 + 20
10 u = 210
1 u = 210 ÷ 10 = 21
Number of coins that David had at first
= 1 u + 1 u + 9
= 2 u + 9
= (2 x 21) + 9
= 42 + 9
= 51
Answer(s): 51
