Among Great-Grand-Ma's papers, an old, worn out bill was found. The bill stated

"... 67.9... dollars for 72 turkeys".

The first and the last digits of the dollar amount had left only faint shadows and were not legible anymore. (Each of the missing digits is represented, here, above, with three dots (...))

Assume that each of the 72 turkeys costed the same amount of money (in dollars and cents).

Determine the price of one turkey at the time Great-Grand-Ma purchased the birds.

What must the first digit (the number of hundreds of dollars) be in ... 67.9...?

What must the last digit (the number of hundreds of dollars) be in... 67.9...?

In a short resume

We are given that 72 turkeys cost a total of **...67.9... dollars**, where the first and last digits of the dollar amount are missing. The task is to figure out what those digits are, assuming that each turkey had the same price (in dollars and cents).

### Step 1: Express the total cost
Let the total cost of 72 turkeys be **$x67.9y**, where **x** is the first missing digit (hundreds place) and **y** is the last missing digit (cents place).

Thus, the total cost is:

\[
\text{Total cost} = 100x + 67.9y \text{ dollars}
\]

### Step 2: Calculate the price per turkey
The price per turkey is obtained by dividing the total cost by 72, so:

\[
\text{Price per turkey} = \frac{x67.9y}{72}
\]

Since the cost per turkey must be a sensible price (in dollars and cents), we need to find values for **x** and **y** such that the result of this division yields a number with exactly two decimal places.

### Step 3: Trial and error with possible digits
- The first digit **x** must make the total cost reasonable. Since we are in the range of hundreds of dollars, we try logical values for **x** that keep the total cost between $100 and $200, for example.
- The last digit **y** must satisfy the condition that when dividing the total cost by 72, the price per turkey has only two decimal places (since we are dealing with dollars and cents).

### Step 4: Determining the correct values
- If **x = 1** (so the cost is $167.9y), we test different values of **y**:

1. **$167.90** / 72 = **$2.3319** (too many decimal places)
2. **$167.91** / 72 = **$2.3321** (still too many decimal places)
3. **$167.92** / 72 = **$2.3322** (still too many decimal places)
4. **$167.93** / 72 = **$2.3324** (still too many decimal places)

This process shows that **$168.00** works, meaning the correct value of **y** is 0.

### Step 5: Conclusion
The total amount of the bill was **$168.00**, and the price of one turkey at the time Great-Grand-Ma purchased them was:

\[
\frac{168.00}{72} = 2.33 \text{ dollars per turkey}.
\]

### Resume:
- The first digit (hundreds place) must be **1**.
- The last digit (cents place) must be **0**.
- Therefore, the total amount was **$168.00**, and the price per turkey was **$2.33**.

---

Would you like further details or have any questions?

Here are 5 related questions to expand on this topic:
1. How does trial and error help in finding the correct price?
2. Could there be more than one solution if additional conditions are changed?
3. What mathematical techniques help to solve similar real-life problems?
4. Why is it important for the price per turkey to have exactly two decimal places?
5. How would the solution change if the number of turkeys were different?

**Tip:** When dividing costs among multiple items, ensure the final price is rounded to match standard currency formatting (dollars and cents).

Among Great-Grand-Ma's papers, an old, worn-out bill was found. The bill stated '... 67.9... dollars for 72 turkeys'. The first and the last digits of the dollar amount had left only faint shadows and were not legible anymore. (Each of the missing digits is represented, here, above, with three dots (...)). Assume that each of the 72 turkeys costed the same amount of money (in dollars and cents). Determine the price of one turkey at the time Great-Grand-Ma purchased the birds. What must the first digit (the number of hundreds of dollars) be in ... 67.9...? What must the last digit (the number of hundreds of dollars) be in... 67.9...?

Solve the problem of finding the missing digits in a total cost of '... 67.9... dollars for 72 turkeys'. Learn how division, decimals, and trial and error can determine the first and last digits of the dollar amount. Ideal for students in Grades 6-8.

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