Mickey's error lies in his initial step of finding the unit price. Let’s go through the correct process step-by-step to understand where he went wrong and what the accurate calculations should be:
### Step 1: Identify the given information
- Total cost for 12 cartons of eggs: [tex]$22.20
- Number of cartons: 12
- Cartons needed: 7
### Step 2: Calculate the correct unit price
To find the unit price (cost per carton), the correct approach is to divide the total cost by the number of cartons. Mathematically, this is expressed as:
\[
\text{Unit Price} = \frac{\text{Total Cost}}{\text{Number of Cartons}}
\]
Substituting the given values:
\[
\text{Unit Price} = \frac{22.20}{12} \approx 1.85
\]
This means each carton of eggs costs approximately $[/tex]1.85.
### Step 3: Calculate the total cost for 7 cartons
Now that we have the correct unit price, we can find the total cost for 7 cartons by multiplying the unit price by the number of cartons needed.
[tex]\[
\text{Total Cost for 7 Cartons} = \text{Unit Price} \times \text{Cartons Needed}
\][/tex]
Substituting the values:
[tex]\[
\text{Total Cost for 7 Cartons} = 1.85 \times 7 = 12.95
\][/tex]
### Step 4: Identify Mickey’s mistake
Mickey’s calculations show:
[tex]\[
\frac{12 \text { cartons }}{22.20} = 0.54
\][/tex]
This indicates he divided the number of cartons (12) by the total cost ([tex]$22.20), which incorrectly gives him a unit price of $[/tex]0.54 per carton.
Mickey should have divided the total cost ([tex]$22.20) by the number of cartons (12), not the other way around.
### Conclusion
By correctly calculating the unit price and the total cost, we can see that the correct unit price is approximately $[/tex]1.85 per carton, and the total cost for 7 cartons is $12.95. This highlights Mickey's error in reversing the division in his initial unit price calculation.
