Math Problem Statement
"Find two numbers whose sum is 81 and whose difference is 35."
Solution
Let the two numbers be and .
Given:
- (Their sum is 81)
- (Their difference is 35)
We now have two equations:
To solve this system of equations, we can add the two equations together:
Simplifying:
Solving for :
Now substitute into the first equation :
Solving for :
Thus, the two numbers are and .
Would you like more details on this solution or have any other questions?
Here are 5 related questions to consider:
- What is the sum and difference of two numbers when given other constraints?
- How can you use substitution to solve systems of equations?
- What methods can you use to solve simultaneous equations?
- Can you derive other relationships between numbers if their sum and difference are known?
- How do different algebraic techniques simplify solving pairs of equations?
Tip: When solving systems of equations, always look for simple operations like addition or subtraction that eliminate one variable.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Formulas
x + y = sum
x - y = difference
2x = sum + difference
Theorems
Solving systems of linear equations by addition
Suitable Grade Level
Grades 6-8
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