Word Problems

Question

1. A village wants to build a community center that is projected to cost 1.2 million dollars. Cost per resident is increased by $3 as it is discovered there are 225 fewer residents than when planning began 2 years ago. What is the revised cost per resident? 

 

 

 

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On a 1287 long road trip in windy conditions, a family calculates their fuel economy to be 18 miles per gallon over the 2 days it takes to reach their destination. On their 2-day return trip, with a similar wind at their backs, their calculations show a fuel economy of 26 miles per gallon.

 

2. Calculate the expected fuel economy of their vehicle in ideal (non-windy) conditions (f) as well as the influence of the wind (w) in miles per gallon.

 

 

2a. Compare how many gallons of fuel they used for the round trip to the expected usage in ideal (non-windy) travel conditions. Which uses more? By how many gallons? Round to the nearest hundreth, if necessary. 

 

Answer 1

Let x₀  be the fuel economy in ideal condition (no wind), Δx - change in fuel economy because of thew wind.

Thus  we have

                        x₀ + Δx = 26

 

                        x₀ - Δx  = 18 

 

By adding these two equations we can find x₀ = 22 mi/gal  ((26 +18)/2). Thus, the family would have spent

 

            1287 /22 = 58.5 gallons traveling in one direction or 117 gallons for the round trip.

 

In reality they have spent  1287/18 = 71.5 gallons in one direction, and 1287/26 = 49.5 gallons for traveling back, or 121 gallons in total. Thus, they could have saved 121 -117 = 4 gallons for the trip in ideal condsitions.

 

 

 

 

Answer 2

1. A village wants to build a community center that is projected to cost 1.2 million dollars. Cost per resident is increased by $3 as it is discovered there are 225 fewer residents than when planning began 2 years ago. What is the revised cost per resident?

Two equations:

(1200000/N)=Po

((1200000/(N-225))= Po +3

this leads us to solve the quadratic:

3N² -675N - 225*1200000 =0

solving for N = 9600 initial number of residents

The amount per resident will be

1200000/9600 = 125 dollars per resident

New or revised amount is

(1200000/(9600-225))= 128 dollars per resident.

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The second part I am working on it.