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Prachi needs between $240$ and $260$ total feet of fence panels. The home improvement store has $24$ short ( $6$ foot) fence panels and $28$ long ( $8$ foot) fence panels in stock. Which of the following combinations of fence panels could she buy? $\newline$ Choose $1$ answer: $\newline$ (A) $6$ short fence panels and $26$ long fence panels $\newline$ (B) $8$ short fence panels and $23$ long fence panels $\newline$ (C) $260$ $0$ short fence panels and $260$ $1$ long fence panels $\newline$ (D) $260$ $2$ short fence panels and $260$ $3$ long fence panels

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Grade 7

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Q. Prachi needs between

240

and

260

total feet of fence panels. The home improvement store has

24

short (

6

foot) fence panels and

28

long (

8

foot) fence panels in stock. Which of the following combinations of fence panels could she buy?

\newline

Choose

1

answer:

\newline

(A)

6

short fence panels and

26

long fence panels

\newline

(B)

8

short fence panels and

23

long fence panels

\newline

(C)

260

0

short fence panels and

260

1

long fence panels

\newline

(D)

260

2

short fence panels and

260

3

long fence panels

Calculate Total Length Option A: Prachi needs a total length of fence that falls between $240$ and $260$ feet. To solve this problem, we will calculate the total length of fence for each given combination of short and long panels. Short panels are $6$ feet long, and long panels are $8$ feet long.
Calculate Total Length Option B: First, let's calculate the total length for option (A): $6$ short fence panels and $26$ long fence panels. The total length can be calculated as $(6 \text{ panels} \times 6 \text{ feet}) + (26 \text{ panels} \times 8 \text{ feet})$ .
Calculate Total Length Option C: For option (A), the calculation is $6 \times 6$ + $26 \times 8$ = $36 + 208$ = $244$ feet. This total falls within the required range of $240$ to $260$ feet.
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ .
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ . For option B, the calculation is $(8 \times 6) + (23 \times 8) = 48 + 184 = 232 \text{ feet}$ . This total does not fall within the required range of $240$ to $260$ feet.
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ . For option B, the calculation is $(8 \times 6) + (23 \times 8) = 48 + 184 = 232 \text{ feet}$ . This total does not fall within the required range of $240$ to $260$ feet. Now, let's calculate the total length for option (C): $27$ short fence panels and $12$ long fence panels. The total length can be calculated as $(27 \text{ panels} \times 6 \text{ feet}) + (12 \text{ panels} \times 8 \text{ feet})$ .
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ . For option B, the calculation is $(8 \times 6) + (23 \times 8) = 48 + 184 = 232 \text{ feet}$ . This total does not fall within the required range of $240$ to $260$ feet. Now, let's calculate the total length for option (C): $27$ short fence panels and $12$ long fence panels. The total length can be calculated as $(27 \text{ panels} \times 6 \text{ feet}) + (12 \text{ panels} \times 8 \text{ feet})$ . For option (C), the calculation is $(27 \times 6) + (12 \times 8) = 162 + 96 = 258 \text{ feet}$ . This total falls within the required range of $240$ to $260$ feet.
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ . For option B, the calculation is $(8 \times 6) + (23 \times 8) = 48 + 184 = 232 \text{ feet}$ . This total does not fall within the required range of $240$ to $260$ feet. Now, let's calculate the total length for option (C): $27$ short fence panels and $12$ long fence panels. The total length can be calculated as $(27 \text{ panels} \times 6 \text{ feet}) + (12 \text{ panels} \times 8 \text{ feet})$ . For option (C), the calculation is $(27 \times 6) + (12 \times 8) = 162 + 96 = 258 \text{ feet}$ . This total falls within the required range of $240$ to $260$ feet. Finally, let's calculate the total length for option (D): $23$ $2$ short fence panels and $23$ $3$ long fence panels. The total length can be calculated as $23$ $4$ .
Calculate Total Length Option D: Next, let's calculate the total length for option B: $8$ short fence panels and $23$ long fence panels. The total length can be calculated as $(8 \text{ panels} \times 6 \text{ feet}) + (23 \text{ panels} \times 8 \text{ feet})$ . For option B, the calculation is $(8 \times 6) + (23 \times 8) = 48 + 184 = 232$ feet. This total does not fall within the required range of $240$ to $260$ feet. Now, let's calculate the total length for option (C): $27$ short fence panels and $12$ long fence panels. The total length can be calculated as $(27 \text{ panels} \times 6 \text{ feet}) + (12 \text{ panels} \times 8 \text{ feet})$ . For option (C), the calculation is $(27 \times 6) + (12 \times 8) = 162 + 96 = 258$ feet. This total falls within the required range of $240$ to $260$ feet. Finally, let's calculate the total length for option (D): $23$ $2$ short fence panels and $23$ $3$ long fence panels. The total length can be calculated as $23$ $4$ . For option (D), the calculation is $23$ $5$ feet. This total falls within the required range of $240$ to $260$ feet.