Math Problem Statement
Solve it in a very simple and easy to understand way
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 .
- Let the number of birds be .
From the given information:
-
Heads equation:
-
Feet equation:
Rabbits have 4 feet, and birds have 2 feet, so:
Step 3: Solve the equations
From the first equation ():
Substitute into the second equation ():
Simplify:
Step 4: Verify the solution
If (rabbits), then (birds).
Check the total number of feet:
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:
- If the total feet were 120, how many rabbits would there be?
- What if the total number of heads was 50?
- If birds had 4 feet instead, how would you solve it?
- What is the minimum possible number of rabbits in any such scenario?
- 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
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