Question

question 23 (3 points)
determine how many boxes of flooring will be needed to cover a 14 feet by 16 feet room if 10% waste is assumed.
first, find the area of the room. the area of the room is _ square feet.
remember that area of a rectangle is length times width.
next, calculate the total square footage of flooring including the 10% waste. hint: multiply the area of the floor by 1.10. the total area including 10% waste is _ square feet.
lastly, calculate the number of boxes of flooring that you will need to buy to ensure that you have enough to cover the floor including at least 10% waste. each box has 10 square feet of flooring. round up to nearest whole number.
question 24 (3 points)
a farmer wants to know how many bags of fertilizer to buy to ensure that his entire field will be covered. he estimates his field to be 3000 feet by 8000 feet. a more accurate measurement of the field results in the field being 3050 feet by 8100 feet. one bag of fertilizer covers 5000 square feet of the field. the farmer uses his estimated numbers to figure out how many bags of fertilizer to buy.
(3000 ft)(8000 ft) = 24000000 ft²
the farmer needs to cover 24000000 ft². since each bag covers 5000 ft², he divides the total square feet of his field by 5000.
24000000 divided by 5000 is 4800. the farmer buys 4800 bags of fertilizer to cover his field. explain the effects that an error in measurement has on the farmers estimated measurements by comparing them to the more accurate measurements.
by using the estimated measurements, the farmer will have enough bags of fertilizer to cover his field.
by using the estimated measurements, the farmer will not have enough bags of fertilizer to cover his field. he will need 142 more bags to cover the entire field.
by using the estimated measurements, the farmer will not have enough bags of fertilizer to cover his field. he will need 141 more bags to cover the entire field.
there is not enough information given in the question to compare the estimated measurements to the more accurate measurements.

Explanation:

Step1: Calculate room area

The room is a rectangle with length $l = 16$ feet and width $w=14$ feet. Using the formula $A = l\times w$, we have $A=16\times14 = 224$ square - feet.

Step2: Calculate area with waste

We assume a 10% waste. So we multiply the room area by 1.10. The total area $A_{total}=224\times1.10 = 246.4$ square - feet.

Step3: Calculate number of boxes

Each box has 10 square - feet of flooring. We divide the total area by the area per box. $n=\frac{246.4}{10}=24.64$. Rounding up to the nearest whole number, we get $n = 25$ boxes.

First, find the accurate area of the field. The accurate dimensions are 3050 feet by 8100 feet, so the accurate area $A_{accurate}=3050\times8100 = 24705000$ square - feet.
The estimated area $A_{estimated}=3000\times8000 = 24000000$ square - feet.
The number of bags needed with accurate measurement $n_{accurate}=\frac{24705000}{5000}=4941$ bags.
The number of bags the farmer bought with estimated measurement $n_{estimated}=4800$ bags.
The difference in the number of bags $\Delta n=4941 - 4800=141$ bags.

Answer:

224
246.4
25

For Question 24: