Math Problem Statement

Solve it in a very simple and easy to understand way

In a cage, there are rabbits and birds. They have 35 heads and 98 feet. The number of rabbits in the cage is?

Solution

Let's solve the problem step by step:

Step 1: Understanding the problem

  • Rabbits and birds are in the cage.
  • Rabbits and birds together have 35 heads. (Each rabbit or bird has 1 head.)
  • They have 98 feet in total. (Rabbits have 4 feet, and birds have 2 feet.)

We need to find the number of rabbits in the cage.


Step 2: Assign variables

  • Let the number of rabbits be xx.
  • Let the number of birds be yy.

From the given information:

  1. Heads equation:

    x+y=35x + y = 35
  2. Feet equation:
    Rabbits have 4 feet, and birds have 2 feet, so:

    4x+2y=984x + 2y = 98

Step 3: Solve the equations

From the first equation (x+y=35x + y = 35):

y=35xy = 35 - x

Substitute y=35xy = 35 - x into the second equation (4x+2y=984x + 2y = 98):

4x+2(35x)=984x + 2(35 - x) = 98

Simplify:

4x+702x=984x + 70 - 2x = 98 2x+70=982x + 70 = 98 2x=282x = 28 x=14x = 14

Step 4: Verify the solution

If x=14x = 14 (rabbits), then y=3514=21y = 35 - 14 = 21 (birds).

Check the total number of feet:

4(14)+2(21)=56+42=984(14) + 2(21) = 56 + 42 = 98

The solution satisfies both equations.


Final Answer:

The number of rabbits in the cage is 14.


Do you want further clarifications or have any questions?
Here are some related questions for practice:

  1. If the total feet were 120, how many rabbits would there be?
  2. What if the total number of heads was 50?
  3. If birds had 4 feet instead, how would you solve it?
  4. What is the minimum possible number of rabbits in any such scenario?
  5. How would the equation change if rabbits had 6 feet?

Tip: Always double-check your answers by substituting values back into the equations.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Systems of Equations

Formulas

x + y = total_heads
4x + 2y = total_feet

Theorems

System of Linear Equations

Suitable Grade Level

Grades 6-8