Question

question 5 (5 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 1200 feet by 1500 feet. a more accurate measurement of the field results in the field being 1202 feet by 1505 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. (1200 ft)(1500 ft)=1800000 ft²
the farmer needs to cover 1800000 ft². since each bag covers 5000 ft², he divides the total square feet of his field by 5000. 1800000 divided by 5000 is 360. the farmer buys 360 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 2 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.
by using the estimated measurements, the farmer will not have enough bags of fertilizer to cover his field. he will need 1 more bag to cover the entire field.

Explanation:

Step1: Calculate accurate field area

The accurate area of the field is $1202\times1505 = 1809010$ square - feet.

Step2: Calculate number of bags needed accurately

Dividing the accurate area by the area covered by one bag: $\frac{1809010}{5000}=361.802$. So, the farmer needs 362 bags (since we can't buy a fraction of a bag).

Step3: Compare with estimated number of bags

The farmer estimated he needed 360 bags. The difference is $362 - 360=2$ bags.

Answer:

B. By using the estimated measurements, the farmer will not have enough bags of fertilizer to cover his field. He will need 2 more bags to cover the entire field.