Mr. Rocco plans to put a 48 foot long fence on one side of his garden. He may buy 6-foot long sections of fence or 8-foot long sections. The 6’ sections cost $12 each and 8’ sections cost $14 each. At the start and at the end of the fence as well as between each section a pole must be placed. The poles cost $3.50 each. If Mr. Rocco used the 8’ sections instead of the 6’ sections, he would save $______ in putting up a 48’ fence.
(6*14 + 7*3.50) - (8*12 + 9*3.50) = ___
yes
To find out how much money Mr. Rocco would save by using 8-foot sections instead of 6-foot sections, we need to calculate the cost for both scenarios.
First, let's calculate the number of sections needed for each scenario.
For the 6-foot sections:
Number of sections = Length of the fence / Length of each section = 48 ft / 6 ft = 8 sections
For the 8-foot sections:
Number of sections = Length of the fence / Length of each section = 48 ft / 8 ft = 6 sections
Next, let's calculate the cost for each scenario.
For the 6-foot sections:
Cost of sections = Number of sections * Cost per section = 8 sections * $12 per section = $96
Cost of poles = Number of sections + 1 = 8 sections + 1 = 9 poles
Cost of poles = Number of poles * Cost per pole = 9 poles * $3.50 per pole = $31.50
Total cost = Cost of sections + Cost of poles = $96 + $31.50 = $127.50
For the 8-foot sections:
Cost of sections = Number of sections * Cost per section = 6 sections * $14 per section = $84
Cost of poles = Number of sections + 1 = 6 sections + 1 = 7 poles
Cost of poles = Number of poles * Cost per pole = 7 poles * $3.50 per pole = $24.50
Total cost = Cost of sections + Cost of poles = $84 + $24.50 = $108.50
To find the savings, subtract the cost of the 8-foot sections from the cost of the 6-foot sections:
Savings = Total cost with 6-foot sections - Total cost with 8-foot sections = $127.50 - $108.50 = $19
Therefore, Mr. Rocco would save $19 by using 8-foot sections instead of 6-foot sections in putting up a 48-foot fence.
To find the amount of money Mr. Rocco would save by using 8' sections instead of 6' sections, we need to calculate the cost of each option and then compare the two.
First, let's determine how many fence sections are needed in each case. Since each section has a length of either 6' or 8', we divide the total length of the fence, 48', by the length of each section.
For the 6' sections:
Number of 6' sections = 48 / 6 = 8 sections
For the 8' sections:
Number of 8' sections = 48 / 8 = 6 sections
Now, let's calculate the cost of putting up the fence using 6' sections:
Cost of fence sections = Number of sections × Cost per section
Cost of fence sections using 6' sections = 8 × $12 = $96
Since there are poles at the start, end, and between each section, the total number of poles needed is the number of sections plus one.
Number of poles using 6' sections = Number of sections + 1
Number of poles using 6' sections = 8 + 1 = 9 poles
Cost of poles = Number of poles × Cost per pole
Cost of poles using 6' sections = 9 × $3.50 = $31.50
The total cost of putting up the fence using 6' sections is the sum of the cost of fence sections and the cost of poles:
Total cost using 6' sections = Cost of fence sections + Cost of poles
Total cost using 6' sections = $96 + $31.50 = $127.50
Now, let's calculate the cost of putting up the fence using 8' sections:
Cost of fence sections using 8' sections = 6 × $14 = $84
Number of poles using 8' sections = Number of sections + 1
Number of poles using 8' sections = 6 + 1 = 7 poles
Cost of poles using 8' sections = 7 × $3.50 = $24.50
Total cost using 8' sections = Cost of fence sections + Cost of poles
Total cost using 8' sections = $84 + $24.50 = $108.50
Finally, to find the amount of money Mr. Rocco would save by using 8' sections instead of 6' sections, we subtract the total cost of using 8' sections from the total cost of using 6' sections:
Amount saved = Total cost using 6' sections - Total cost using 8' sections
Amount saved = $127.50 - $108.50 = $19
Therefore, Mr. Rocco would save $19 by using 8' sections instead of 6' sections to put up a 48' fence.