Two girls were selling candy. They have $1.07 in change to begin. Their first customer said that before he could buy anything, he needed change for half a dollar. One of the girls looked and said that they didn't have the change. Then the customer asked if they had change for a quarter, but again, no. The customer asked if they had change for a dime- the answer was again no. The girls said they didn't even have change for a nickel. If they have 7 coins, what are they?

Let's analyze the problem step by step, focusing on the key information given:

1. **Total Value**: The girls have a total of $1.07.
2. **Coins**: They have 7 coins in total.
3. **No Change for Half a Dollar**: This means they don't have enough coins (or the right combination of coins) to give 50 cents.
4. **No Change for a Quarter**: They can't make 25 cents with their coins.
5. **No Change for a Dime**: They can't make 10 cents with their coins.
6. **No Change for a Nickel**: They can't make 5 cents with their coins.

### Key Observations:

- They have 7 coins, and the total is $1.07. 
- No combinations of their coins can add up to 50 cents, 25 cents, 10 cents, or 5 cents. This means they probably don't have any nickels, dimes, or quarters.
- The only coin that they could still have is **pennies** (1 cent) and **one dollar coin** ($1).

### Deduction:

If they can't make change for a nickel, it suggests that **none of the coins** are nickels or smaller multiples of 5 (which would be consistent with dimes and quarters as well). Therefore, the coins are likely:

- **1 dollar coin** (worth $1.00)
- **6 pennies** (worth 6 cents)

This gives a total of:

\[
1 \text{ dollar} + 6 \times 1 \text{ cent} = 1.00 + 0.06 = 1.06
\]

But they need $1.07, so something is off. Let me reconsider the scenario to make sure we cover the final

Learn how to solve a coin puzzle where two girls have $1.07 and 7 coins, but can't make change for 50 cents, 25 cents, 10 cents, or even 5 cents. Explore logical reasoning and combinatorics as you determine the coins in their possession. Suitable for students in Grades 5-7.

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