Nick has 9 more 50-cent coins than 20-cent coins. After he used 10 of his 50-cent coins, the total value of 50-cent coins is $2.20 more than the total value of 20-cent coins. How many coins did he have at first?
| |
50¢ |
20¢ |
| Before |
1 u + 9 |
1 u |
| Change |
- 10 |
|
| After |
1 u - 1 |
1 u |
| |
50¢ |
20¢ |
| Number |
1 u - 1 |
1 u |
| Value |
50 |
20 |
| Total value |
50 u - 50 |
20 u |
$1 = 100¢
$2.20 = 220¢
Number of 50¢ coins in the end
= 1 u + 9 - 10
= 1 u - 1
Total value of 50¢ coins in the end
= 50 x (1 u - 1)
= 50 u - 50
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 10 50-cent coins, the value of 50-cent coins is 220¢ more than the value of 20-cent coins. If another 220¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 50 = 20 u + 220
50 u - 20 u = 220 + 50
30 u = 270
1 u = 270 ÷ 30 = 9
Number of coins that Nick had at first
= 1 u + 1 u + 9
= 2 u + 9
= (2 x 9) + 9
= 18 + 9
= 27
Answer(s): 27
