Answer:
- wheat: $3.61 per bu
- corn: $3.61 per bu
- rye: $1.91 per bu
Step-by-step explanation:
You want to know the price per bushel for wheat, corn, and rye, given the sales ...
- 5 bu wheat + 2 bu corn + 3 bu rye for $31.00
- 2 bu wheat + 3 bu corn + 5 bu rye for $27.60
- 3 bu wheat + 5 bu corn + 2 bu rye for $32.70
Equations
Using x, y, and z for price per bushel of wheat, corn, and rye, respectively, the given sales tell us ...
- 5x +2y +3z = 31.00
- 2x +3y +5z = 27.60
- 3x +5y +2z = 32.70
Solution
The easiest way to solve a system of equations like this is to make use of the matrix manipulation capabilities of a calculator. The attached calculator display shows the reduction of the augmented matrix of coefficients to "reduced row-echelon form". That puts the solution in the last column:
x = y = 3.61, z = 1.91
The price per bushel for wheat and corn is the same: $3.61; the price per bushel for rye is $1.91.
__
Additional comment
The second attachment shows a solution using a graphing calculator. In this solution, an expression for z based on the first equation is used in the remaining two equations, which then tell us the values of x and y.
If you add all of the equations, you get 10x +10y +10z = 91.30, which gives you ...
x + y + z = 9.13
This can be solved for any variable you may want to substitute into any pair of the equations. This approach avoids any messy fractions.
<95141404393>
