word problem challenge

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word problem challenge

Category: Case Study

Subcategory: Mathematics

Level: College

Pages: 3

Words: 825

Author’s Name
Lecturer
Course Title
Due Date
Math 1105 Word Problem Challenge
Question one
1400 square feet
804545494665½ acre

Gate
Height is 8 feet
12 inches thick
Material labor equipment total
Cost per square foot 3.17 4.57 .06 7.80
Cost per block 2.81 4.06 .05 6.92
Cost per linear foot 25.30 36.74 .54 62.58
(Get-a-quote.net)
Concrete block is assumed to measure 12’ by 8” by 16” (Get-a-quote.net)
1 foot is 12 inches; therefore 8 * 12 = 96 inches
96/16= 6 bricks high
For width 1 brick is 8”
Required width is 12”
Total bricks is 1 and ½
Total 12” by 12” by 96”
6+3 =9; 9 * 6.92 =62.28
Area of the plot is ½ acre which is also equal to 21780 square ft.
Gate area by actual measurements is 13.12ft * 8ft =104.96 ft.
Square root of 21780 is 147.58
147.58 – 104.96=1766.688
1766.688/12=147.224
147.224 * 62.28 * 4= 36676.44
Reinforcement steel
Wielded wire mesh measuring 4” by 4” at total cost of 1.71 dollars (Get-a-quote.net)
Total metal covered height 4ft / 12”= 0.333 ft.
147.58/4= 36.895
96/4 =24
24* 36.895=885.48 * 4= 3541.92
16”= 1.71 DOLLARS; 3541.92 * 1.71/24 =378.5427
TOTAL COST OF WALL 378.5427 + 36676.44 =37054.99
Assumptions
Concrete block measures 12’ by 8” by 16” (Get-a-quote.net)
The plot is squared
Wall is squared around the plot
Measures used are of the USA standard
Average household of 4 people consumes 400 gallons of water per day
2 months = approximately 60 days
60 days = 24000 gallons
1 cubic ft. = 7480 gallons
24000 gallons are therefore = 3208.556 square ft.
6housemates 1 month
4 housemates. 2 months
2 housemates. 4 months
The data above is regressed using MS Excel
  Coefficients Intercept 7 X Variable 1 -1.28571 Y (housemates) = 7 – 1.28571x (months)
A unit increase in the number of users leads to a decrease in the time period by 1.28571 months
Assumptions made
1 cubic ft. = 7480 gallons
An average household of 4 people consumes 400 gallons of water a day
There are four people in the household (Abramson 67)
The food was purchased from COSTCO consisting of real freeze dried and dehydrated fruits costing 424.995 dollars for one person in 6 months (Get-a-quote.net).
For 4 persons it will be 424.995 * 4 which adds up to 1699.98 dollars.
The total amount used is therefore 38753 dollars, which makes the 87500 dollars enough.
Question two
Costs in the first year
Total cost of seeds =74 dollars (Costco.com)
Cost of truck (ford) =32000 dollars
Cost of 4 bags of organic fertilizer=80 dollars (Author’s computation)
Interest rate on loan = 3.3% (Data.worldbank.org)
Total = 32154
Took a loan of 35000
Interest =1155
32154+1155=33309 Benefits in the first year
Total population = 1488 (City-data.com)
Customer population (10%)=148
Estimated families (4 per family)=148/4=37.2
1 track =20 standard boxes
I track = 20 weeks
In a week it delivers twice (20 + 17.2)
Number of weeks = 9* 4 = 36
36 * 2 =72 times
Cost of fuel =72 * 2.59= 186.48
Breakeven price for first year( where profits =losses)
33309+186.48=p *(36*37.2)
P=25.01

Profits in year 2
3% * 1488=44.64
148.8+ 44.64=193.44
193.44/4=48.36
48.36 * 36 =1740.96
Assume no fluctuation and that she maintains the same price throughout
1740.96 * 25.01 – 186.48=43355
Year 3
44.64 +193.44=238.08
238.08/4=59.52
59.52 *36= 2142.72
2142.72 * 25.01-186.48=53403
Number of customers
239 profits
53403 194 43355 149 0 Redress the results above in MS Excel to obtain the following:
  Coefficients
Intercept 145.8836
X Variable 1 0.001492
Y (customers) =145.8836 + 0.001492X (profits)
A unit increase in the profits increases the number of customers by 0.001492
Profits for year 7: in year 3 customer population = 238.08
238.08 +44.64 * 4 = 416.64
416.64/4 =104.16
104.16 *36 =3749.76
3749.76-186.48=3563.28
Add 2% revenue (2% of 3749.76) = 74.995
=3638.76
lefttop

It is assumed that she grows crops 3 months in a year

Seeds
Orders kale tomatoes beet carrots asparagus spinach
22 1 2 4 2 4 2 31 3 2 3 1 2 3 A regression analysis is done as shown below
  Coefficients
Intercept 40
X Variable 1 0
X Variable 2 0
X Variable 3 0
X Variable 4 0
X Variable 5 -4.5
X Variable 6 0
The seeds bought are not dependent on the orders made
If in he consecutive period 29 seeds were needed to feed 13 percent of the population which is 193.44 to feed 25 percent which is 372 will require55.76 or 56 seeds
Assumptions made
In the first year she was to buy one packet of seeds or each crop
There are four people in the household
Number of customers was in decimal form for accuracy purposes. Otherwise it should be rounded off to the nearest figure.
Constraints Faced: The data used was secondary data due to the time and financial constraints involved in using primary data.
In the food price estimation, the results do not really reflect the real world experience as tastes and preferences of people change over time.

Works Cited
Abramson, Marcie F. Painless Math Word Problems. Hauppauge, N.Y: Barron’s Educational Series, 2010. Print
Bluman, Allan G. Math Word Problems Demystified. New York [N.Y.: McGraw-Hill, 2011. Internet resource.
City-data.com, Geahart Oregon: Population of Gearhart. N.p., 2015. Web. 13 Dec. 2015.
Costco.com, ‘Canned & Prepared Foods’. N.p., 2015. Web. 13 Dec. 2015.
Data.worldbank.org,’Current Bank Lending Rates In USA’.N.p., 2015. Web.13 Dec.2015.
Get-a-quote.net, ‘Get-A-Quote.Net — Get a Building Cost Quotation Online’. N.p., 2015. Web. 13 Dec. 2015.