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Jess will plant up to 27 acres on her farm with wheat and corn. More than 5 acres will be planted with wheat.

Let [tex] w [/tex] represent the number of acres of wheat and [tex] c [/tex] represent the number of acres of corn. Identify two inequalities that represent this situation.

A. [tex] w + c \leq 27 [/tex]
B. [tex] c \ \textless \ 5 [/tex]
C. [tex] w - c \leq 27 [/tex]
D. [tex] w \ \textgreater \ 5 [/tex]

Sagot :

GinnyAnswer
To solve this problem, we need to derive a pair of inequalities based on the given conditions.

1. Total Acreage Constraint:
- Jess will plant up to 27 acres in total with either wheat or corn. This means the combined number of acres for wheat (\(w\)) and corn (\(c\)) cannot exceed 27 acres.
- Mathematically, this can be represented as:
[tex]\[ w + c \leq 27 \][/tex]
- Therefore, inequality A \(w + c \leq 27\) is correct.

2. Wheat Constraint:
- It is stated that more than 5 acres will be planted with wheat. This means the number of acres for wheat must be greater than 5.
- Mathematically, this can be represented as:
[tex]\[ w > 5 \][/tex]
- Therefore, inequality D \(w > 5\) is also correct.

Having evaluated the given options, the two inequalities that correctly represent Jess's planting constraints are:
[tex]\[A. \quad w + c \leq 27\][/tex]
[tex]\[D. \quad w > 5\][/tex]

Therefore, the correct answer is:
[tex]\[ A. \, w + c \leq 27 \][/tex]
[tex]\[ D. \, w > 5 \][/tex]
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