A total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.
Step-by-step explanation:
Step 1:
Assume the number of non-commercial vehicles to be x and the number of commercial vehicles to be y.
It is given that for every 14 non-commercial vehicles there will be 5 commercial vehicles. So a ratio can be formed as follows;
[tex]\frac{x}{14}[/tex] = [tex]\frac{y}{5}[/tex], cross multiplying, we get [tex]5 x=14 y[/tex], take this as equation 1.
Step 2:
It is also given that there were 108 more non-commercial vehicles than commercial vehicles. So
[tex]x=y+108[/tex], take this as equation 2.
If we solve equations 1 and 2, we will get the values of x and y.
Step 3;
Substitute equation 2 in equation 1.
[tex]5(y+108)=14 y[/tex],
[tex]5y+540 = 14y[/tex],
[tex]y = \frac{540}{9} = 60[/tex].
Substitute [tex]y = 60[/tex] in equation 2.
[tex]x=60+108 = 168[/tex].
So x = 168 and y = 60.
So a total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.
