Chapter 5.2, Problem 19E

To determine

To find: The number ofacres of wheat and corn planted by the farmer

Answer to Problem 19E

Wheat is planted on $45acres$ of land and Corn is planted on $135acres$ of land

Explanation of Solution

Given:

  $\begin{array}{l}w+c=180\\ c=3w\end{array}$

Calculation:

Let $w$ be the area (in acres) on which wheat is planted and $c$ be the area (in acres) on which corn is planted

  $\begin{array}{l}w+c=180\\ c=3w\end{array}$

Substituting value of $c$ obtained from second equation, in equation first equation,

  $\begin{array}{l}4w=180\\ w=45\end{array}$

Use the value obtained in second equation to find the value of $c$ ,

  $\begin{array}{l}c=3w\\ =3(45)\\ =135\end{array}$

verify that $\left(w,c\right)=\left(45,135\right)$ is solution to the system of equations

  $\begin{array}{l}w+c=180\\ 45+135=180\\ 180=180\\ c=3w\\ 135=3\left(45\right)\\ 135=135\end{array}$

Thus, wheat is planted on $45acres$ of land and corn is planted on $135acres$ of land

Conclusion:

Hence, the wheat is planted on $45acres$ of land and corn is planted on $135acres$ of land