The area of Stanley Park in Vancouver is 391 hectares. The forested area is 141 hectares more than the rest of the park. What is the area of each part of the park?

The system of equations that models this situation is:

A. [tex]f = r - 141[/tex] and [tex]f = r + 391[/tex]

B. [tex]r = f - 391[/tex] and [tex]r = 141 - f[/tex]

C. [tex]f - r = 391[/tex] and [tex]f + r = 141[/tex]

D. [tex]f + r = 391[/tex] and [tex]f - r = 141[/tex]

To solve the problem of finding the area of each part of Stanley Park, we can create a system of equations based on the information given:

1. Since the forested area (f) is 141 hectares more than the rest of the park (r), we can write the first equation as:
[tex]\[
f = r + 141
\][/tex]

2. The total area of Stanley Park is 391 hectares, which means the sum of the forested area and the rest of the park equals 391 hectares. This gives us the second equation:
[tex]\[
f + r = 391
\][/tex]

Now we can solve these two equations step-by-step:

Step 1: Substitute the expression for [tex]$ f $[/tex] from the first equation into the second equation.

Since [tex]$ f = r + 141 $[/tex], substitute this into the equation [tex]$ f + r = 391 $[/tex]:
[tex]\[
(r + 141) + r = 391
\][/tex]

Step 2: Simplify the equation.

Combine like terms:
[tex]\[
2r + 141 = 391
\][/tex]

Step 3: Solve for [tex]$ r $[/tex].

Subtract 141 from both sides of the equation:
[tex]\[
2r = 250
\][/tex]

Divide both sides by 2 to find [tex]$ r $[/tex]:
[tex]\[
r = 125
\][/tex]

Step 4: Substitute back to find [tex]$ f $[/tex].

Use the first equation [tex]$ f = r + 141 $[/tex]:
[tex]\[
f = 125 + 141
\][/tex]

Calculate [tex]$ f $[/tex]:
[tex]\[
f = 266
\][/tex]

Therefore, the forested area is 266 hectares, and the rest of the park is 125 hectares.