Chapter 6.2, Problem 42PPE

To determine

To determine how many acres of each crop should the farmer plant.

Answer to Problem 42PPE

The farmer should plant ‘152’ acres of corn, ‘112’ acres of tomatoes and ‘56’ acres of sunflowers.

Explanation of Solution

Given :

A farmer grows corn, tomatoes, and sunflowers on a 320-acre farm. This year, the farmer wants to plant twice as many acres of tomatoes as acres of sunflowers. The farmer also wants to plant 40 more acres of corn than of tomatoes.

Calculation :

Let the area (in acres) for growing corn = $\text{'}x\text{'}$

Let the area (in acres) for growing tomatoes = $\text{'}y\text{'}$

Let the area (in acres) for growing sunflowers = $\text{'}z\text{'}$

Since, the total area available for farming is 320 acres.

Therefore, $x+y+z=320$ ………..(i)

Now, farmer wants to plant twice as many acres of tomatoes as acres of sunflowers.

Hence, $y=2z$ or $z=\frac{y}{2}$ …………..(ii)

Also, farmer also wants to plant 40 more acres of corn than of tomatoes.

Hence, $x=y+40$ ……………(iii)

Substituting (ii) and (iii) in (i),

  $\begin{array}{l}x+y+z=320\\ \Rightarrow y+40+y+\frac{y}{2}=320\\ \Rightarrow \frac{5y}{2}=320-40=280\\ \Rightarrow 5y=280\times 2\\ \Rightarrow 5y=560\\ \Rightarrow y=112\end{array}$

Since, $x=y+40$

  $\Rightarrow x=112+40=152$

And, $z=\frac{y}{2}$

  $\Rightarrow z=\frac{112}{2}=56$

Conclusion :

Hence, the farmer should plant ‘152’ acres of corn, ‘112’ acres of tomatoes and ‘56’ acres of sunflowers.