Question

there are 150 more passenger cars than trucks on the highway. for every 10 passenger cars there are 7 trucks. how many trucks are on the highway?

Answer 1

There would be 500 passenger cars and 350 trucks.

Explanation:

In order to find this, we need to create a system of equations. Start by making the number of passenger cars as x and the number of trucks at y. Now the first equation can be the difference of the two.

x - y = 150

The second equation can make use of the proportion. If we multiply by the opposites we'll get the difference of 0.

7x - 10y = 0

Now we multiply the first equation by -10 and add together to solve for x.

-10x + 10y = -1500

7x - 10y = 0

-------------------

-3x = -1500

x = 500

Now we can find the amount of trucks by using either equation.

x - y = 150

500 - y = 150

-y = -350

y = 350

Answer 2

500

Explanation:

Given: P = 150 - T where P is passenger cars and T is trucks

10P = 7T ⇔ P =
`(7T)/(10)`

Plug in equation 2 into equation 1:

`(7T)/(10)` = 150 - T

Solving for T, we get 500