Ivan has 7 more 20-cent coins than 10-cent coins. After he used 13 of his 20-cent coins, the total value of 20-cent coins is $2.80 more than the total value of 10-cent coins. How many coins did he have at first?
| |
20¢ |
10¢ |
| Before |
1 u + 7 |
1 u |
| Change |
- 13 |
|
| After |
1 u - 6 |
1 u |
| |
20¢ |
10¢ |
| Number |
1 u - 6 |
1 u |
| Value |
20 |
10 |
| Total value |
20 u - 120 |
10 u |
$1 = 100¢
$2.80 = 280¢
Number of 20¢ coins in the end
= 1 u + 7 - 13
= 1 u - 6
Total value of 20¢ coins in the end
= 20 x (1 u - 6)
= 20 u - 120
Total value of 10¢ coins in the end
= 10 x 1 u
= 10 u
After using 13 20-cent coins, the value of 20-cent coins is 280¢ more than the value of 10-cent coins. If another 280¢ is added to the 10-cent coins, the total value of 20-cent coins and 10-cent coins will be the same.
20 u - 120 = 10 u + 280
20 u - 10 u = 280 + 120
10 u = 400
1 u = 400 ÷ 10 = 40
Number of coins that Ivan had at first
= 1 u + 1 u + 7
= 2 u + 7
= (2 x 40) + 7
= 80 + 7
= 87
Answer(s): 87
