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Chapter 3: Problem 43

There were 1223 endangered plant and animal species in the United States. There were 243 more endangered plant species than animal species. How many plant species and how many animal species were considered endangered in \(2016 ?\)

Short Answer

Expert verified
There were 733 endangered plant species and 490 endangered animal species.

Step by step solution

01

Define Variables

Define the variables to represent the number of endangered plant and animal species. Let the number of endangered animal species be represented by \( A \) and the number of endangered plant species be represented by \( P \).
02

Set Up Equations

Create two equations based on the information given in the problem:1) There are a total of 1223 endangered species, so \( P + A = 1223 \).2) There are 243 more endangered plant species than animal species, so \( P = A + 243 \).
03

Substitute One Equation into the Other

Substitute the second equation into the first equation. Replace \( P \) in the first equation with \( A + 243 \), leading to:\[ (A + 243) + A = 1223 \]
04

Solve for Animal Species (A)

Combine like terms and solve for \( A \):\[ A + 243 + A = 1223 \]\[ 2A + 243 = 1223 \]Subtract 243 from both sides:\[ 2A = 980 \]Divide by 2:\[ A = 490 \]
05

Solve for Plant Species (P)

Use the value of \( A \) to find \( P \). Substitute \( A = 490 \) back into the equation \( P = A + 243 \):\[ P = 490 + 243 \]\[ P = 733 \]
06

Verify the Solution

Check the solution by adding the numbers of plant and animal species:\[ P + A = 733 + 490 = 1223 \]This matches the total given in the problem, so the solution is verified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Variable Definitions
Starting with any problem involving systems of equations, it's important to clearly define the variables. Here, we need to find the number of endangered plant and animal species.

Let's use:
  • Let the number of endangered animal species be represented by \(A\).
  • Let the number of endangered plant species be represented by \(P\).


Defining your variables helps give a clear direction for setting up and solving equations.
Equation Substitution
Next, we set up the equations based on the problem. We have:
  • The total number of endangered species (plants + animals) is \(1223\). So, \(P + A = 1223\).
  • There are 243 more endangered plant species than animal species, expressed as \(P = A + 243\).


To make solving easier, substitute the second equation into the first equation.

Replace \(P\) in \(P + A = 1223\) with \(A + 243\), resulting in:

\((A + 243) + A = 1223\)

This simplifies the problem to a single equation with one variable.
Combining Like Terms
Combining like terms helps to simplify the equation and makes it easier to solve.

Start with the simplified substitution equation:

\(A + 243 + A = 1223\)

Combine like terms (\(A\) terms) to get:

\(2A + 243 = 1223\)

Next, to isolate \(A\), subtract 243 from both sides:

\(2A = 980\)

Then, divide by 2:

\(A = 490\)

You've now found the number of endangered animal species.
Solving Linear Equations
After solving for one variable, use this value to find the other.

We found \(A = 490\). Now, substitute \(A\) back into the equation for \(P\):

\(P = A + 243\)

Replace \(A\) with \(490\):

\(P = 490 + 243\)

This gives \(P = 733\).

Finally, check your solution by adding the known values of \(A\) and \(P\):

\(P + A = 733 + 490 = 1223\)

This matches the total given in the problem, confirming the solution is correct.

Thus, there are 733 endangered plant species and 490 endangered animal species.

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