Question

Any help on the top question?

Answer 1

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;

$\frac{x}{14}$ = $\frac{y}{5}$, cross multiplying, we get $5 x=14 y$, take this as equation 1.

Step 2:

It is also given that there were 108 more non-commercial vehicles than commercial vehicles. So

$x=y+108$, 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.

$5(y+108)=14 y$,

$5y+540 = 14y$,

$y = \frac{540}{9} = 60$.

Substitute $y = 60$ in equation 2.

$x=60+108 = 168$.

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.