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 =
Let the area (in acres) for growing tomatoes =
Let the area (in acres) for growing sunflowers =
Since, the total area available for farming is 320 acres.
Therefore,
Now, farmer wants to plant twice as many acres of tomatoes as acres of sunflowers.
Hence,
Also, farmer also wants to plant 40 more acres of corn than of tomatoes.
Hence,
Substituting (ii) and (iii) in (i),
Since,
And,
Conclusion :
Hence, the farmer should plant ‘152’ acres of corn, ‘112’ acres of tomatoes and ‘56’ acres of sunflowers.
Chapter 6 Solutions
High School Math 2015 Common Core Algebra 1 Student Edition Grade 8/9
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