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Question
Fencing Prices
ABC Fencing (Fence length in feet) Total Cost Billed
100 24,000
120 29,200
180 44,800
250 63,000
Mr. Edwards is replacing an existing fence on his farm that is 6 feet high. Reliable Fence Company charges $8,000 for building materials and $225 per foot of fencing. The function y = $225x + $8,000 represents the total charge. ABC Fence Company bases the total charges solely on the length of the fence. The table shows some input and output values for various lengths of fencing. Which statement BEST compares the price of fencing per foot for the two companies?
Responses
A ABC Fence Company charges $15 more per foot of fencing.ABC Fence Company charges $15 more per foot of fencing.
B Reliable Fence Company charges $25 more per foot of fencing.Reliable Fence Company charges $25 more per foot of fencing.
C ABC Fence Company charges $35 more per foot of fencing.ABC Fence Company charges $35 more per foot of fencing.
D Both companies charge the same price per foot of fencing.
To compare the price of fencing per foot for the two companies, we need to divide the total cost by the length of the fence.
For ABC Fencing, the total cost is given in the table. Let's calculate the cost per foot for each length:
- For 100 feet of fencing: $24,000 / 100 = $240 per foot
- For 120 feet of fencing: $29,200 / 120 = $243.33 per foot
- For 180 feet of fencing: $44,800 / 180 = $248.89 per foot
- For 250 feet of fencing: $63,000 / 250 = $252 per foot
Now, let's compare this to Reliable Fence Company, which charges $225 per foot.
It is clear that ABC Fence Company charges significantly more per foot of fencing compared to Reliable Fence Company. The difference varies for different fence lengths, but it is always more than $15 and $25.
Therefore, the correct statement is:
C) ABC Fence Company charges $35 more per foot of fencing.