Formulate and solve systems of three linear equations in three variables using elimination

Question

A farmer rotates wheat, corn, soybean crops on her farm. The farmer produces 293 bushels of produce and sells them for a total of $1557. Wheat costs $8 a bushel. Corn costs $4 a bushel. Soybeans cost $9 a bushel. If the farmers crops yield 4.75 times more corn than wheat, how many bushels of each crop does the farmer produce?

Answer 1

Let S= bushels of soybeans and W = wheat and C = corn. From the text convert the words into an algebraic equation.

9S+8W+4C=1557

S+W+C=293

C=4.75W ... solve to find C= 207.1 bushels

Use substitution to get

9S+27W=1557 ... S=173-3W ... solve to find S= 42.1 bushels

S+5.75W=293 ... 173+2.75W=293 ... solve to find W= 43.6 bushels