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 1

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 14:5

n = number of non commercial vehicles during september

c = number of commercial vehicles during septemer

We know that if we add the commercial (c) vehicles with 108 we will have the non-commercial (n) vehicles

n = c + 108

so we need to do the equivalent ratios to know which is the value of c

$\frac{14}{5} =\frac{n}{c}$

replace n

$\frac{14}{5} =\frac{c+108}{c}$

$14c = 5 ( 108 + c)\\14c =540 + 5c\\14c - 5c = 540\\9c = 540\\c = \frac{540}{9} \\c = 60$

Then the number of commercial vehicles is 60 and the number of non commercial vehicles is:

n = 60 + 108

n = 168

There are 168 non commercial vehicles during september

We 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 9

28:10   difference 18

42:15   difference 27

56:20   difference 36

70:25   difference 45

84:30   difference 54

98:35   difference 63

112:40   difference 72

126:45   difference 81

140:50   difference 90

154:55   difference 99

168:60   difference 108

As the difference is 108 we have that there are 168 non commercial vehicles and 60 commercial vehicles during the month of september