Sam has the following types of coins in his wallet.
| Types of coins | Number of coins |
|---|---|
| 5 ¢ | 3 |
| 10 ¢ | 2 |
| 20 ¢ | 2 |
| 50 ¢ | 1 |
| $1 | 1 |
He took out 3 coins from his wallet and donated them to charity.
Which one of the following amounts could not be the amount taken out of his wallet?
(1) $\$1.55$
(2) $\$0.70$
(3) $\$0.60$
(4) $\$0.55$
(4)
Check each option by forming the amount with 3 coins:
Option (1): $\$1.55$ (155¢)$$100\text{ ¢} + 50\text{ ¢} + 5\text{ ¢} = 155\text{ ¢}$$ This is possible using one $1 coin, one 50¢ coin, and one 5¢ coin.
Option (2): $\$0.70$ (70¢)$$50\text{ ¢} + 10\text{ ¢} + 10\text{ ¢} = 70\text{ ¢}$$ This is possible using one 50¢ coin and two 10¢ coins.
Option (3): $\$0.60$ (60¢)$$50\text{ ¢} + 5\text{ ¢} + 5\text{ ¢} = 60\text{ ¢}$$ This is possible using one 50¢ coin and two 5¢ coin.
Option (4): $\$0.55$ (55¢)
To get 55¢, the sum must end in 5. This means that one 5¢ coin must be used.
Remaining amount needed: $55\text{ ¢} - 5\text{ ¢} = 50\text{ ¢}$.
We need to make 50¢ with 2 other coins.
Possible combinations for 50¢ with 2 coins from the remaining:
- $20\text{ ¢} + 20\text{ ¢} = 40\text{ ¢}$ (Not 50¢)
- $20\text{ ¢} + 10\text{ ¢} = 30\text{ ¢}$ (Not 50¢)
- $50\text{ ¢}$ coin itself (This is 1 coin, not 2)
No combination of 2 coins (excluding the 5¢ coin already used) sums to 50¢.
Since 55¢ cannot be formed by taking out exactly 3 coins, this is the amount that could not be taken out.
The answer is option (4).
