Given that 1text{ acre} = 4{,}840text{ square yards}, 1text{ rod} = 5.5text{ yards}, and 1text{ furlong} = 40text{ rods}, which...

1. Translate the problem requirements: Convert 1 acre (given in square yards) to square furlongs by building a conversion chain from yards → rods → furlongs, then squaring the linear conversion to get area conversion
2. Build the linear conversion chain: Use the given relationships to convert from yards to rods to furlongs step by step
3. Convert to area units: Square the linear conversion factor to transform from linear furlongs to square furlongs
4. Apply conversion and approximate: Convert 1 acre using the derived conversion factor and round to match the closest answer choice

Execution of Strategic Approach

1. Translate the problem requirements

Let's start by understanding what we need to do in everyday terms. We have 1 acre that we know equals 4,840 square yards, and we want to find out how many square furlongs that same area represents.

Think of this like converting between different measurement systems - similar to how you might convert feet to meters, but we're dealing with area measurements here. We need to build a "conversion bridge" from square yards to square furlongs using the relationships given.

The key insight is that we're converting an area measurement, so we'll need to be careful about how linear conversions become area conversions.

Process Skill: TRANSLATE

2. Build the linear conversion chain

Let's build our conversion step by step using the given relationships:

First, let's see what we know:

• 1 rod = 5.5 yards
• 1 furlong = 40 rods

Now let's convert yards to furlongs by going through rods:

Step 1: Convert yards to rods
If 1 rod = 5.5 yards, then 1 yard = \(\frac{1}{5.5}\) rods

Step 2: Convert rods to furlongs
If 1 furlong = 40 rods, then 1 rod = \(\frac{1}{40}\) furlongs

Step 3: Combine the conversions
1 yard = \(\left(\frac{1}{5.5}\right)\) rods = \(\left(\frac{1}{5.5}\right) \times \left(\frac{1}{40}\right)\) furlongs = \(\frac{1}{5.5 \times 40}\) furlongs
1 yard = \(\frac{1}{220}\) furlongs

So our linear conversion factor is: 1 yard = \(\frac{1}{220}\) furlongs

3. Convert to area units

Here's where we need to be careful! We have a linear conversion (yards to furlongs), but we need an area conversion (square yards to square furlongs).

When we convert area measurements, we need to square the linear conversion factor.

Since 1 yard = \(\frac{1}{220}\) furlongs, then:
1 square yard = \(\left(\frac{1}{220}\right)^2\) square furlongs
1 square yard = \(\frac{1}{48,400}\) square furlongs

This makes sense - since furlongs are much longer than yards, square furlongs should be much larger area units than square yards, so we expect many square yards to equal just a small fraction of a square furlong.

4. Apply conversion and approximate

Now we can convert 1 acre to square furlongs:

1 acre = 4,840 square yards

Using our conversion factor:
4,840 square yards = \(4,840 \times \frac{1}{48,400}\) square furlongs
= \(\frac{4,840}{48,400}\) square furlongs
= \(\frac{1}{10}\) square furlongs
= 0.1 square furlongs

Looking at our answer choices: ["0.05","0.1","1","10","22"]

Our calculated value of 0.1 square furlongs matches exactly with choice B.

Final Answer

The area equal to 1 acre is 0.1 square furlongs, which corresponds to answer choice B.

Common Faltering Points

Errors while devising the approach

Students often fail to recognize that converting between area units requires squaring the linear conversion factor. They might think that if 1 yard = \(\frac{1}{220}\) furlongs, then 1 square yard = \(\frac{1}{220}\) square furlongs, missing the crucial step of squaring the conversion factor to get \(\frac{1}{48,400}\).

Students may get confused about whether they're converting from smaller to larger units or vice versa. Since furlongs are much longer than yards, they might incorrectly assume that square furlongs should be a smaller unit than square yards, leading to an inverted conversion factor.

The problem requires converting through an intermediate unit (rods). Students might attempt to find a direct relationship between yards and furlongs or miss one of the given conversion relationships entirely, leading to an incomplete conversion chain.

Errors while executing the approach

When calculating \(5.5 \times 40 = 220\), students might make simple multiplication errors, leading to incorrect denominators like 200 or 240, which would cascade through the entire solution.

Even if students recognize they need to square the linear conversion factor, they might incorrectly calculate \(\left(\frac{1}{220}\right)^2 = \frac{1}{440}\) instead of \(\frac{1}{48,400}\), often by just doubling the denominator instead of squaring it.

When simplifying \(\frac{4,840}{48,400}\), students might make errors in recognizing that this equals \(\frac{1}{10}\). They might incorrectly simplify to other fractions or fail to reduce it properly, especially if they made earlier calculation errors.

Errors while selecting the answer

No likely faltering points - the final calculation yields 0.1, which directly matches answer choice B with no additional interpretation needed.