To find out whether Cameron's solution is reasonable, we need to check the calculation of the area of the wall using the given dimensions.
The dimensions of the wall are:
- Length = 16.5 feet
- Height = 8.625 feet
To find the area: Area = Length × Height = 16.5 feet × 8.625 feet
Now let's perform the multiplication:
16.5 × 8.625 = 142.40625 square feet
It appears that Cameron's calculation of 1423.125 square feet is incorrect, as it does not match the correct value derived from the multiplication.
Now, analyzing the options:
-
"Cameron’s solution is reasonable because there are four decimal places in the factors and four decimal places in the product."
- Irrelevant because the calculation itself is incorrect.
-
"Cameron’s solution is reasonable because there are three decimal places in the factors and three decimal places in the product."
- Also irrelevant because the calculation itself is incorrect.
-
"Cameron’s solution is unreasonable because 17 times 9 is 153, and 153 is not close to his product."
- This response is incorrect because it doesn't relate to the given dimensions.
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"Cameron’s solution is unreasonable because 10 times 10 is 100, and 100 is not close to his product."
- While the comparison is not directly relevant, this option does at least imply the reasonableness of estimating the area.
The most accurate conclusion is that Cameron's solution is unreasonable because the computed area (1423.125 square feet) is significantly larger than the area calculated (142.40625 square feet). Thus, while the reasoning in the explanations doesn't entirely align, the best reasoning here would lead us to conclude that one's understanding of the multiplication is flawed or the interpretation of the dimensions is misplaced.
Ultimately, the area is off and Cameron did not reasonably calculate it. Therefore, the response that identifies this as unreasonable is appropriate even though the arithmetic example of comparing "10 times 10" could be misleading.