David has 10 more 50-cent coins than 20-cent coins. After he used 14 of his 50-cent coins, the total value of 50-cent coins is $2.50 more than the total value of 20-cent coins. How many coins did he have in the end?
|
50¢ |
20¢ |
Before |
1 u + 10 |
1 u |
Change |
- 14 |
|
After |
1 u - 4 |
1 u |
|
50¢ |
20¢ |
Number |
1 u - 4 |
1 u |
Value |
50 |
20 |
Total value |
50 u - 200 |
20 u |
$1 = 100¢
$2.50 = 250¢
Number of 50¢ coins in the end
= 1 u + 10 - 14
= 1 u - 4
Total value of 50¢ coins in the end
= 50 x (1 u - 4)
= 50 u - 200
Total value of 20¢ coins in the end
= 20 x 1 u
= 20 u
After using 14 50-cent coins, the value of 50-cent coins is 250¢ more than the value of 20-cent coins. If another 250¢ is added to the 20-cent coins, the total value of 50-cent coins and 20-cent coins will be the same.
50 u - 200 = 20 u + 250
50 u - 20 u = 250 + 200
30 u = 450
1 u = 450 ÷ 30 = 15
Number of coins that David had in the end
= 1 u + 1 u - 4
= 2 u - 4
= (2 x 15) - 4
= 30 - 4
= 26
Answer(s): 26