We are tasked with finding 16 coins that add up to a value of $1.67. The denominations of U.S. coins are as follows:

• Penny (1 cent or 0.01)
• Nickel (5 cents or 0.05)
• Dime (10 cents or 0.10)
• Quarter (25 cents or 0.25)

We need to figure out the exact combination of these coins to sum up to $1.67 while using exactly 16 coins.

Let’s solve this step by step.

Key Ideas:

1. The total value is 167 cents (because $1.67 = 167 cents).
2. We need exactly 16 coins.

Let's try to find the right combination of coins through trial and error, considering the values of each type of coin.

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Solution:

We can try a combination of mostly larger denominations (quarters, dimes) and fill in the rest with smaller denominations like pennies.

One possible solution is:

• 6 Quarters = 6 × 25 = 150 cents
• 1 Dime = 1 × 10 = 10 cents
• 1 Nickel = 1 × 5 = 5 cents
• 8 Pennies = 8 × 1 = 8 cents

Now, let's check the total:

$6 \times 25 + 1 \times 10 + 1 \times 5 + 8 \times 1 = 150 + 10 + 5 + 8 = 167 \text{ cents}$

So, we have exactly 167 cents with 16 coins.

Final Answer:

The 16 coins are:

• 6 quarters
• 1 dime
• 1 nickel
• 8 pennies

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:

1. What other combinations of coins can make up the same total value of $1.67?
2. What if the number of coins was 10 instead of 16—how would you change the combination?
3. How would you solve this if one coin type wasn't available, like dimes?
4. Can you calculate the total weight of these coins given the mass of each type?
5. What is the minimum number of coins that can sum up to exactly $1.67?

Tip: When solving coin-related problems, start with the largest denomination to minimize the number of coins, then fill in with smaller denominations.