One of the guest rooms in my house has two walls that are 15'6" by 8 ft, and two that are 12'3" by 8 ft. When buying paint for the walls, I estimated the wall area to be about 450 sq. ft. Find my percent area.
First I need to find the total area of the wall -- I did this by doubling the wall space for each. For the first one I calculated it to be 240'^2 16". For the second I calculated it to be 120'^2 6"
Then I converted the inches into feet as much as I could and that all came to 361'^2 8"
Then to compute the percent error I did 450 ft^2 - 361ft^2 divided by 361ft^2
My answer is 2.4% but the correct answer is 1.4%.
What have I done incorrectly?
2 * 8 (15.5 + 12.25) = 444
(450 - 444) / 444 = .01351 ≈ 1.4%
there appear to be several arithmetic errors in your calculations
... but your method is correct
I guess I don't understand where you are getting the 2 * 8?
Would you see it if Scott had written his calculation as
8*15.5 + 8*15.5 + 8*12.25 + 8*12.25 ?
which is 8*(15.5+15.5+12.25+12.25)
= 8*2(15.5+12.25) , which is what Scott started with.
Yes, I see it now - I wasn't equating the 15'5" to 15 1/2' and the 12'3" to 12.25' - I was doing it in a much harder way - thank you!
It seems like there are two main areas where you made mistakes in your calculations:
1. Converting inches to feet: When converting the measurements from inches to feet, it's important to divide by 12, since there are 12 inches in a foot. It looks like you may have made an error in your conversion.
For the first wall, 15'6" by 8 ft would be (15 + 6/12) ft by 8 ft, which is (15.5 ft) by 8 ft.
For the second wall, 12'3" by 8 ft would be (12 + 3/12) ft by 8 ft, which is (12.25 ft) by 8 ft.
2. Calculating the total wall area: To find the total wall area, you correctly doubled the wall space for each wall. However, it seems like there might be a mistake in your calculations when finding the areas of the individual walls.
For the first wall, the area would be (15.5 ft) * (8 ft) = 124 ft^2.
For the second wall, the area would be (12.25 ft) * (8 ft) = 98 ft^2.
Adding these two areas together: 124 ft^2 + 98 ft^2 = 222 ft^2.
Now, let's calculate the percent error:
Percent error = (|Actual Value - Estimated Value| / Actual Value) * 100
Using the correct estimated value of 222 ft^2, the percent error would be:
(|450 ft^2 - 222 ft^2| / 222 ft^2) * 100 = (228 ft^2 / 222 ft^2) * 100 ≈ 102.7%.
Therefore, the correct percent error is around 102.7%, not 1.4% or 2.4%.