# word problem challenge

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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.

Wait! word problem challenge paper is just an example!

= 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.

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