Daniel has 3 more 50-cent coins than 20-cent coins. After he used 4 of his 50-cent coins, the total value of 50-cent coins is $3.10 more than the total value of 20-cent coins. How many coins did he have in the end?
| |
50¢ |
20¢ |
| Before |
1 u + 3 |
1 u |
| Change |
- 4 |
|
| 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¢
$3.10 = 310¢
Number of 50¢ coins in the end
= 1 u + 3 - 4
= 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 4 50-cent coins, the value of 50-cent coins is 310¢ more than the value of 20-cent coins. If another 310¢ 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 + 310
50 u - 20 u = 310 + 50
30 u = 360
1 u = 360 ÷ 30 = 12
Number of coins that Daniel had in the end
= 1 u + 1 u - 1
= 2 u - 1
= (2 x 12) - 1
= 24 - 1
= 23
Answer(s): 23
