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The surface area of two fields is 300 dunam.

From the first field people picked up 80 ton of oranges, and from the second field people picked up 50 ton of oranges.

The amount of oranges for every dunam at the first field is 100 kilograms less then at the second field.

Find the surface area and the amount of oranges to every dunam at every field.

 

Firstly for the benefit of others, A dunam is a unit of area that is commonly used in the Turkish region and also in Israel.  It is equal to about 900m^2

By ton I am going to assume that you mean a metric tonne.

100kg = 0.1 tonne

 

Field B        Let it be B dunam

Produces 50 tonnes

Let production be x tonnes/ dunam

so      x*B=50

 

Field A      Let it be A dunam      

Produces 80 tonne

(x-0.1) tonnes per dunam

so       (x-0.1)*A=80

 

But A+B=300

so substitute     A=300-B

 

(x-0.1)(300-B)=80                   and   x*B=50

                                                            B= 50/x

 

\((x-0.1)(300-\frac{50}{x})=80  \\ x(x-0.1)(300-\frac{50}{x})=80x  \\ (x-0.1)(300x-50)=80x  \\ 300x^2-50x-30x+5=80x\\ 300x^2-80x+5=80x\\ 300x^2-160x+5=0\\ 60x^2-32x+1=0\\ 60x^2-30x-2x+1=0\\ 30x(2x-1)-1(2x-1)=0\\ (30x-1)(2x-1)=0\\ x=\frac{1}{30} \qquad or \qquad x=\frac{1}{2}\\ \)

 

If x=1/30 then the production for field A is (1/30-0.1) which is negative so this is a nonsense solution.

 

Hence      x=0.5

Field B produces 0.5 tonnes/dunam     and it produces a total of 50 tonnes.

50 divided by 0.5 = 100 dunam

 

Field A produces 0.5-0.1=0.4 tonnes per dunam   and it produces 80 tonnoes.

80 divided by  0.4 = 200 dunam

 

So Field A is 200 dunam and it produces 400 Kg/dunam

and Field B is 100 dunam and it produces 500 Kg/dunam