Question

In a car dealership, all of the vehicles are either

Answer 1

Answer:

The number of sedans before any vehicle was sold is 168

Step-by-step explanation:

Let's define the variables:

x = number of sedans

y = number of SUVs

We know that:

"If 36 sedans are sold and 36  SUVs are added, there will be an equal number  of sedans and SUVs"

If 36 sedans are sold, the new number of sedans is:

x - 36

if 36 SUVs are added, the new number of SUVs is

y + 36

And these numbers are equal, then:

x - 36 = y + 36

We also know that:

" If 8 SUVs are sold and 8  sedans are added, there will be twice as many

sedans as SUVs. "

If 8 SUVs are sold, the new number of SUVs will be:

y - 8

If 8 sedans are added, the new number of sedans wil be:

x + 8

From this we can write the equation:

(x + 8) = 2*(y - 8)

x + 8 = 2*y - 16

Then we have two equations:

x - 36 = y + 36

x + 8 = 2*y - 16

We want to find the number of sedans, x, then we need to isolate the other variable in one of the equations, let's isolate y in the first one:

Let's isolate x in the first one:

x - 36 - 36 = y

x - 72 = y

Now we can replace it in the other equation:

x + 8 = 2*y - 16

x + 8 = 2*(x - 72) - 16

Now we can solve this for x.

x + 8 = 2*x - 144 - 16

8 + 144 + 16 = 2x - x

168  = x

The number of sedans before any vehicle was sold is 168