Question 1139506



All I can say is...You better appreciate this!  It’s going to take awhile.


s = number of soybean acres
c = number of corn acres
w = number of wheat acres


s + c + w = 500  {total acres of his farm is 500}
120s + 100c + 80w = 51,000  {price per acre times number of acres = total profit}
c = 2s  {he plants twice as many acres of corn as soybeans}


-80s - 80c - 80w = -40,000   {multiplied 1st equation by-80}
120s + 100c + 80w = 51,000   {2nd equation stays the same}
-—————————————
40s + 20c = 11,000   {added the two equations, cancelling the w’s}


c = 2s   {3rd equation from above}
40s + 20c = 11,000   {equation created above}


40s + 20(2s) = 11,000   {substituted 2s in for c}
40s + 40s = 11,000   {multiplied}
80s = 11,000   {added}
s = 137.5   {divided by 80}


c = 2s   {equation from above}
c = 2(137.5)   {substituted 137.5, in for s, into c = 2s}
c = 275   {multiplied}


s + c + w = 500  {1st equation above}
137.5 + 275 + w = 500   {substituted 137.5 in for s and 275 in for c}
w + 412.5 = 500   {combined like terms}
w = 87.5   {subtracted 412.5 from each side}


137.5 acres of soybeans, 275 acres of corn, and 87.5 acres of wheat
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