The Superintendent of Highways is further interested in the numbers of commercial vehicles that frequently use the county’s highways. He obtains information from the Department of Motor Vehicles for the month of September and finds that for every 14 non-commercial vehicles, there were 5 commercial vehicles. If there were 108 more non-commercial vehicles than commercial vehicles, how many of each type of vehicle frequently use the county’s highways during the month of September?

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Question:

The Superintendent of Highways is further interested in the numbers of commercial vehicles that frequently use the county’s highways. He obtains information from the Department of Motor Vehicles for the month of September and finds that for every 14 non-commercial vehicles, there were 5 commercial vehicles. If there were 108 more non-commercial vehicles than commercial vehicles, how many of each type of vehicle frequently use the county’s highways during the month of September?

Answer:During the month of september there where 60 commercial vehicles and 168 non commercial vehicles. Step-by-step explanation:we have that the ratio between non-commercial vehicles and commercial vehicles is 14:5n = number of non commercial vehicles during septemberc = number of commercial vehicles during septemerWe know that if we add the commercial (c) vehicles with 108 we will have the non-commercial (n) vehiclesn = c + 108so we need to do the equivalent ratios to know which is the value of c[tex]\frac{14}{5} =\frac{n}{c}[/tex]replace n[tex]\frac{14}{5} =\frac{c+108}{c}[/tex][tex]14c = 5 ( 108 + c)\\14c =540 + 5c\\14c - 5c = 540\\9c = 540\\c = \frac{540}{9} \\c = 60[/tex]Then the number of commercial vehicles is 60 and the number of non commercial vehicles is:n = 60 + 108n = 168There are 168 non commercial vehicles during septemberWe can solve this problem in another way by calculating equivalent ratios until we fulfill the condition that the non commercial vehicles equals the commercial vehicles plus 108 then we have:14:5 difference 928:10 difference 1842:15 difference 2756:20 difference 3670:25 difference 4584:30 difference 5498:35 difference 63112:40 difference 72126:45 difference 81140:50 difference 90154:55 difference 99168:60 difference 108As the difference is 108 we have that there are 168 non commercial vehicles and 60 commercial vehicles during the month of september

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