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