I was given a series of questions I got through all but the last point. I need help on letter L, not figuring out how to solve, just how to write it in an equation.

Here is the main problem and sub problems and answers,

Your company must use a transportation service to shuttle their corporate partners from the airport for a quarterly meeting. Crespo Transportation Service charges $32 initially plus $8 per mile for every mile traveled. Siera Transportation Service charges $24 initially plus $10 per mile for every mile traveled.

i) Write an equation in two variables (x & y) that illustrates the costs for the Crespo Transportation Service.

Y=32+8x

j) Write an equation in two variables (x & y) that illustrates the costs for the Siera Transportation Service.

Y=24+10x

k) If the trip is 3 miles, how much does each one charge? If the trip is 6 miles, how much does each one charge? Explain
If the trip is 3 miles then Crespo transportation services would charge $56
Y=32+8x
Y=32+8(3)
Y=32+24
Y=56
For Siera transportation service if the trip is 3 miles then the total charge would be $54
Y=24+10x
Y=24+10(3)
Y=24+30
Y=54

l) At what mileage are both services charging the same rate? Explain
To find the mileage that would equal the same rate I would

I answered all but the last one and cannot figure how to write the equation;can you guide me?

all your answers are correct.

For the last part:

set the two y values equal
24 + 10x = 32 + 8x
2x = 8
x = 4

check: if x = 4
for the first equation,
y = 32 + 8(4) = 64

for the second equation
y = 24 + 10(4) = 64

Checks !!

Sure! To find the mileage at which both services are charging the same rate, we need to set the equations of the two services equal to each other.

Let's start with the equation for Crespo Transportation Service:
Y = 32 + 8x

And the equation for Siera Transportation Service:
Y = 24 + 10x

To find the mileage at which both services charge the same rate, we'll set the equations equal to each other:

32 + 8x = 24 + 10x

Now, we can solve this equation to find the value of x, which represents the mileage where both services charge the same rate.

First, let's simplify the equation by combining like terms:
8x - 10x = 24 - 32

Simplifying further, we get:
-2x = -8

To isolate x, we divide both sides of the equation by -2:
(-2x) / -2 = (-8) / -2
x = 4

Therefore, at a mileage of 4 miles, both Crespo Transportation Service and Siera Transportation Service will charge the same rate.

To write the equation, we substitute x = 4 into either of the original equations. Let's use the equation for Crespo Transportation Service:
Y = 32 + 8x

Substituting x = 4, we get:
Y = 32 + 8(4)
Y = 32 + 32
Y = 64

So at a mileage of 4 miles, both services will charge a total of $64.