Math Problem Statement
The average of two numbers is 7 and three times the difference between them is 18 find the numbers
Solution
Let the two numbers be and .
Step 1: Use the given information to set up equations.
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Average of two numbers: The average of and is 7, so: Multiplying both sides by 2:
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Three times the difference: Three times the difference between them is 18, so: Dividing both sides by 3:
Step 2: Solve the system of equations.
We now have the following two equations:
Add these two equations to eliminate :
Now, substitute into the equation :
Final Answer:
The two numbers are and .
Would you like further details or have any questions?
Here are some related questions for practice:
- If the average of two numbers is 12 and the difference is 5, what are the numbers?
- The sum of two numbers is 30, and their difference is 10. Find the numbers.
- The average of two numbers is 9, and three times their difference is 15. Find the numbers.
- The difference between two numbers is 8, and their sum is 24. What are the numbers?
- Two numbers have an average of 5, and their product is 12. What are the numbers?
Tip: When solving systems of equations, combining them by addition or subtraction can help eliminate one variable, simplifying the solution.
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Math Problem Analysis
Mathematical Concepts
Algebra
System of Linear Equations
Formulas
Average formula: (x + y) / 2 = average
Difference formula: x - y = difference
Theorems
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Suitable Grade Level
Grades 6-8