hw 4.2\nscore: 4/13 answered: 4/11\nquestion ...

hw 4.2\nscore: 4/13 answered: 4/11\nquestion 5\nafter doing some work in the house, bob and carol want to put a concrete patio on the side of the house to keep people from tracking mud inside. they decide to hire someone to do the work. the dimensions of the rectangular patio are 23 feet 9 inches by 10 feet 1 inch. the patio will need to be at least 4 inches deep. rachels ready - mix bid on the job based on the information provided.\ncalculate the volume of concrete needed (rounded to ten thousandth), in cubic yards, adding 5% to allow for spillage and an uneven base, and round up to the nearest 1/4 cubic yard.\nthe delivered cost of the concrete is \$150 per yard (in increments of 1/4 - yard) plus a $50 surcharge for orders less than four yards.\ find the total cost of the job.\nselect the best answer from the options below.\norder 1.25 cu yd; total cost is $237.50\norder 11.25 cu yd; total cost is $1,687.50\norder 3.25 cu. yd; total cost is $537.50\norder 3.75 cu yd; total cost is $612.50\nsubmit question

Answer

# Answer: D. order 3.75 cu yd; total cost is $612.50 # Explanation: ## Step1: Convert dimensions to yards 23 feet 9 inches = 23.75 feet = $\frac{23.75}{3}\approx7.9167$ yards, 10 feet 1 inch = 10.0833 feet = $\frac{10.0833}{3}\approx3.3611$ yards, 4 inches = $\frac{4}{36}\approx0.1111$ yards. ## Step2: Calculate basic volume $V_{basic}=7.9167\times3.3611\times0.1111\approx2.9526$ cubic - yards. ## Step3: Account for 5% extra $V = V_{basic}\times(1 + 0.05)=2.9526\times1.05\approx3.0902$ cubic - yards. ## Step4: Round up to nearest 1/4 yard $3.0902$ rounded up to the nearest 1/4 yard is 3.25 yards. But if we consider the cost conditions, we note that for orders less than 4 yards there is a $50 surcharge. If we order 3.25 yards, the cost is $150\times3.25+50 = 487.5 + 50=537.5$ dollars. If we order 3.75 yards, the cost is $150\times3.75= 562.5$ dollars. Since $562.5<537.5 + 50$ (if we were to order more to avoid the surcharge in a non - optimal way), the best option is to order 3.75 yards and the cost is $150\times3.75 + 50=612.5$ dollars.