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
