A ''Collector's Coin Set'' contains a one - dollar coin, a fifty - cent, a quarter (= 25 cents), a dime ( = 10 cents), a nickel (= 5 cents), and penny ( = 1 cent). The Coin Sets are sold for the combined face price of the currency. If Colin buys as many Coin Sets as he can with the `$25` he has, how much change will Colin have left over?

Answer

To solve the problem step by step, we need to determine the total cost of one collector's coin set and how many sets Colin can buy with his $25. Finally, we will calculate how much change he has left over.

### Step 1: Calculate the total value of one coin set
A collector's coin set contains the following coins:
- 1 dollar coin = 100 cents
- 50-cent coin = 50 cents
- Quarter = 25 cents
- Dime = 10 cents
- Nickel = 5 cents
- Penny = 1 cent

Now, we will add these values together to find the total value of one coin set in cents.

\[ \text{Total value of one coin set} = 100 + 50 + 25 + 10 + 5 + 1 = 191 \text{ cents} \]

### Step 2: Convert Colin's total money into cents
Colin has $25. To convert this amount into cents, we multiply by 100 (since 1 dollar = 100 cents).

\[ \text{Total money in cents} = 25 \times 100 = 2500 \text{ cents} \]

### Step 3: Determine how many coin sets Colin can buy
Next, we will find out how many complete coin sets Colin can buy with his 2500 cents. We do this by dividing the total amount of money by the cost of one coin set.

\[ \text{Number of coin sets} = \frac{2500}{191} \]

Calculating this gives:

\[ \text{Number of coin sets} = 13 \quad \text{(quotient)} \]

### Step 4: Calculate the total cost of the coin sets Colin can buy
Now, we multiply the number of coin sets by the cost of one coin set to find out how much money Colin spends.

\[ \text{Total cost} = 13 \times 191 = 2483 \text{ cents} \]

### Step 5: Calculate the change left over
Finally, we will find out how much change Colin has left after buying the coin sets. We do this by subtracting the total cost from the total amount of money Colin had.

\[ \text{Change left} = 2500 - 2483 = 17 \text{ cents} \]

### Final Answer
Colin will have **17 cents** left over as change.

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