Questions: Adam will plant up to 41 acres on his farm with wheat and corn. Fewer than 28 acres will be planted with corn. Let w represent the number of acres of wheat and c represent the number of acres of corn. Identify two inequalities that represent this situation. A. w>28 B. c<28 C. w-c ≤ 41 D. w+c ≤ 41

Adam will plant up to 41 acres on his farm with wheat and corn. Fewer than 28 acres will be planted with corn. Let w represent the number of acres of wheat and c represent the number of acres of corn. Identify two inequalities that represent this situation. A. w>28 B. c<28 C. w-c ≤ 41 D. w+c ≤ 41
Transcript text: Apex Learning Algebra Il Sem 1 4.3.3 Quiz: Linear Systems of Inequalities Question 4 of 10 Adam will plant up to 41 acres on his farm with wheat and corn. Fewer than 28 acres will be planted with corn. Let $w$ represent the number of acres of wheat and $c$ represent the number of acres of corn. Identify two inequalities that represent this situation. A. $w>28$ B. $c<28$ C. $w-c \leq 41$ D. $w+c \leq 41$
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Solution

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Solution Steps

To identify the inequalities that represent the given situation, we need to translate the constraints into mathematical expressions. The first constraint is that Adam will plant up to 41 acres with wheat and corn combined, which translates to \( w + c \leq 41 \). The second constraint is that fewer than 28 acres will be planted with corn, which translates to \( c < 28 \).

Solution Approach
  1. Translate the total acreage constraint into an inequality.
  2. Translate the corn acreage constraint into an inequality.
Step 1: Translate the Total Acreage Constraint

Adam will plant up to 41 acres with wheat and corn combined. This can be expressed as: \[ w + c \leq 41 \]

Step 2: Translate the Corn Acreage Constraint

Fewer than 28 acres will be planted with corn. This can be expressed as: \[ c < 28 \]

Final Answer

The two inequalities that represent the given situation are: \[ \boxed{w + c \leq 41} \] \[ \boxed{c < 28} \]

For the multiple-choice question, the correct answers are:

  • \( D: w + c \leq 41 \)
  • \( B: c < 28 \)
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