- Convert Tyler's cake weight (\(8 \frac{1}{8}\) lbs) into pounds and ounces: \(8 \text{ lb } 2 \text{ oz}\).
- Subtract \(3\) lb \(11\) oz from Tyler's weight using the relationship \(\text{Tyler's weight} - 3 \text{ lb } 11 \text{ oz} = \text{Theresa's weight}\).
- Borrow \(1\) lb (\(16\) oz) from the remaining pounds to handle the negative ounce value resulting from \(2 \text{ oz} - 11 \text{ oz}\).
- Conclude that Theresa's cake weighs \(\boxed{4 \text{ lb } 7 \text{ oz}}\).
Explanation
- Analyze Tyler's Cake Weight
To determine the weight of Theresa's cake, we start by noting the weight of Tyler's cake, which is \(8 \frac{1}{8}\) pounds. Since we are working with ounces and pounds, we first convert the fractional pound part into ounces. Knowing that \(1\) pound is equivalent to \(16\) ounces, we calculate the number of ounces in \(\frac{1}{8}\) of a pound:
\[\frac{1}{8} \times 16 \text{ oz} = 2 \text{ oz}.\]
Thus, Tyler's cake weighs \(8\) pounds and \(2\) ounces.
- Set up the Subtraction Equation
We know that Tyler's cake weighs \(3\) pounds \(11\) ounces more than Theresa's cake. If we denote Theresa's cake weight as \(W_{Th}\), we have the relationship:
\[\text{Tyler's weight} = W_{Th} + 3 \text{ lb } 11 \text{ oz}.\]
To find \(W_{Th}\), we subtract \(3\) lb \(11\) oz from Tyler's weight:
\[W_{Th} = 8 \text{ lb } 2 \text{ oz} - 3 \text{ lb } 11 \text{ oz}.\]
- Complete the Calculation
Now, we perform the subtraction. First, we subtract the pounds: \(8 \text{ lb} - 3 \text{ lb} = 5 \text{ lb}\). Next, we consider the ounces: \(2 \text{ oz} - 11 \text{ oz} = -9 \text{ oz}\). Since we cannot have a negative number of ounces, we convert \(1\) pound from our \(5\) pounds into ounces:
\[5 \text{ lb } - 9 \text{ oz} = 4 \text{ lb } + (16 \text{ oz} - 9 \text{ oz}) = 4 \text{ lb } 7 \text{ oz}.\]
Therefore, Theresa's cake weighs \(4\) pounds and \(7\) ounces.
Examples
Understanding how to convert and subtract units is essential for everyday tasks, such as cooking, shopping, or construction. For instance, if you are scaling a recipe that uses imperial units but need to adjust for the size of your pans or the number of guests, knowing how to subtract weights like pounds and ounces ensures your ingredients are perfectly balanced. This logic applies whenever you need to find the difference between two quantities given in composite units.