Question

In a parking lot, 20% of the vehicles are trucks

and the remainder are cars. If there are 30 more

cars than trucks, how many cars are in the

parking lot?

Answer 1

The answer is 40 units

Answer 2

Answer: 40

Step-by-step explanation:

To answer this question, it is important to think about the ratio of cars:trucks

we know that 20% of all the vehicles are trucks

which means that 80% of all the vehicles must be cars

this means that the ratio of cars to trucks is 80%:20%

- you may drop the percent and simplify the fraction to 4:1 at this point

---- 80/20 = 8/2 = 4/1 (just to show where that fraction came from)

so now we know:

ratio of cars to trucks = 4:1

cars = 30 + trucks

now you can set up an equation to solve for the missing information

`(4)/(1)` =
`(30+Trucks)/(Trucks)` --> where we have listed cars simply as 30 + trucks to only have one variable in the equation

from here you can simplify the fraction
`(30+trucks)/(trucks) = (trucks)/(trucks) +(30)/(trucks)`

at this point you will see that
`(trucks)/(trucks)` can simplify to 1

so now you have
`(4)/(1) = 1+(30)/(trucks)`

at this point, simplify 4/1 to just 4

4 = 1 +
`(30)/(trucks)`

subtract 1 from both sides

`3 = (30)/(trucks)`

now you can write
`(30)/(trucks)` as
`(1)/(trucks) * 30`

from here, divide both sides by 30 to get

`(1)/(10) = (1)/(trucks)`

since these fractions must be equal, we now know that there must be 10 trucks

using 30 + trucks = cars --> we know that there are 40 cars

let's check using the other given info

if there are 10 trucks and 40 cars = 50 vehicles total

20% of 50 = 10 ; which proves that 20% of all vehicles in the lot are trucks and we have the right answer

ANSWER: there are 40 Cars in the parking lot