An old book listed that $72$ turkeys were bought for $\$\square.\square\square$ each, at a total cost of $\$\square 67.9\square.$
What was the cost of each turkey, if each $\square$ is a smudge that represents some unreadable digit?

Note: The $\square$ digits are not all the same.

We are given that 72 turkeys were bought, with the price per turkey being \$$\square.\square\square$, and the total cost of all the turkeys is \$$\square67.9\square$. The task is to determine the cost of each turkey while accounting for the smudged digits.

### Step 1: Express the relationship mathematically

Let:
- $ p = \square.\square\square $ represent the price of one turkey.
- $ T = \square67.9\square $ represent the total cost.

We know the total cost $ T $ is obtained by multiplying the price per turkey $ p $ by the number of turkeys:
\[
T = 72 \times p
\]

### Step 2: Analyze the total cost

The total cost is given as \$$\square67.9\square$. The total is in the form of a four-digit number: $\square67.9\square$, where the first digit and the last digit are smudged. So, the total cost could be anywhere between \$1679.01 and \$9679.99.

### Step 3: Possible price per turkey

Since we know the total cost is approximately $ \square67.9\square $, let's estimate the price per turkey. 

- If the total cost were approximately \$467.90, the price per turkey would be:
\[
p = \frac{467.90}{72} \approx 6.50
\]
- If the total cost were approximately \$967.90, the price per turkey would be:
\[
p = \frac{967.90}{72} \approx 13.44
\]
Thus, the price per turkey is likely between \$6.50 and \$13.44.

### Step 4: Refine the total cost range

We also know that the total cost $ T = \square67.9\square $, meaning the hundreds place is 6, which narrows down the total cost range. The total cost should be between \$667.90 and \$767.99.

### Step 5: Solve for price

Testing these values of the total cost:
- If $ T = 667.90 $, then:
\[
p = \frac{667.90}{72} \approx 9.27
\]
This gives a price per turkey of approximately \$9.27.

Thus, the cost of each turkey is approximately **\$9.27**.

Would you like further details or explanations?

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**Related questions:**
1. How would the solution change if the number of turkeys was different?
2. Can you verify the total cost if one turkey cost \$9.27?
3. What if the price per turkey was rounded to the nearest cent?
4. How would this calculation work if the total cost had different smudged digits?
5. How do you solve similar problems when the digits are unreadable?

**Tip:** Always double-check your calculations when working with approximations, as rounding can sometimes introduce small errors!

An old book listed that 72 turkeys were bought for $\square.\square\square each, at a total cost of $\square 67.9\square. What was the cost of each turkey, if each $\square is a smudge that represents some unreadable digit? Note: The $\square digits are not all the same.

Find the cost of each turkey when the total cost and price per turkey have unreadable digits. Learn how to estimate the solution with algebra and arithmetic, and calculate the price of each turkey with a detailed step-by-step approach. Suitable for Grades 7-10.

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