Answer :
To identify the two inequalities that correctly represent the planting situation described, we can break down the problem into two main statements:
1. Jess will plant more than 5 acres with wheat.
2. Jess will plant up to 27 acres on her farm with both wheat and corn.
Let's represent these statements mathematically.
### Inequality 1: More than 5 acres will be planted with wheat
This statement tells us that the number of acres of wheat, denoted by [tex]\( w \)[/tex], must be greater than 5. Therefore, we can write the inequality as:
[tex]\[ w > 5 \][/tex]
### Inequality 2: Jess will plant up to 27 acres on her farm with wheat and corn
This statement indicates that the combined total of the acres planted with wheat and corn should not exceed 27 acres. Mathematically, this can be expressed as:
[tex]\[ w + c \leq 27 \][/tex]
where [tex]\( c \)[/tex] represents the number of acres planted with corn.
Now, let's match these mathematical inequalities to the given options:
- Option A: [tex]\( c < 5 \)[/tex] - This inequality does not relate to the given information about the total acres or the specific requirements for wheat planting.
- Option B: [tex]\( w > 5 \)[/tex] - This matches our first inequality.
- Option C: [tex]\( w + c \leq 27 \)[/tex] - This matches our second inequality.
- Option D: [tex]\( w - c \leq 27 \)[/tex] - This inequality does not accurately represent the total acreage constraint.
Thus, the correct pair of inequalities that represent the given planting situation are:
[tex]\[ w > 5 \][/tex]
and
[tex]\[ w + c \leq 27 \][/tex]
So the correct options are:
B. [tex]\( w > 5 \)[/tex]
and
C. [tex]\( w + c \leq 27 \)[/tex]
1. Jess will plant more than 5 acres with wheat.
2. Jess will plant up to 27 acres on her farm with both wheat and corn.
Let's represent these statements mathematically.
### Inequality 1: More than 5 acres will be planted with wheat
This statement tells us that the number of acres of wheat, denoted by [tex]\( w \)[/tex], must be greater than 5. Therefore, we can write the inequality as:
[tex]\[ w > 5 \][/tex]
### Inequality 2: Jess will plant up to 27 acres on her farm with wheat and corn
This statement indicates that the combined total of the acres planted with wheat and corn should not exceed 27 acres. Mathematically, this can be expressed as:
[tex]\[ w + c \leq 27 \][/tex]
where [tex]\( c \)[/tex] represents the number of acres planted with corn.
Now, let's match these mathematical inequalities to the given options:
- Option A: [tex]\( c < 5 \)[/tex] - This inequality does not relate to the given information about the total acres or the specific requirements for wheat planting.
- Option B: [tex]\( w > 5 \)[/tex] - This matches our first inequality.
- Option C: [tex]\( w + c \leq 27 \)[/tex] - This matches our second inequality.
- Option D: [tex]\( w - c \leq 27 \)[/tex] - This inequality does not accurately represent the total acreage constraint.
Thus, the correct pair of inequalities that represent the given planting situation are:
[tex]\[ w > 5 \][/tex]
and
[tex]\[ w + c \leq 27 \][/tex]
So the correct options are:
B. [tex]\( w > 5 \)[/tex]
and
C. [tex]\( w + c \leq 27 \)[/tex]
