Algebra Puzzle – Challenge 54
This is a great math challenge for those who enjoy solving math and algebra challenges! The solution is also given.
![Algebra Puzzle – Challenge 54](https://www.effortlessmath.com/wp-content/uploads/2020/04/Challenge-54-512x240.jpg)
Challenge:
If \(9a^2 – b^2 = 11\) and a and b are positive integers, what is the value of \(a – b\)?
A- \(-5\)
B- \(-3\)
C- 3
D- 5
E- 7
The Absolute Best Book to challenge your Smart Student!
![](https://www.effortlessmath.com/wp-content/uploads/2020/04/answer.png)
The correct answer is B.
Factorize \(9a^2 – b^2\) and 11
(3a – b) (3a + b) = 11 × 1
Therefore, 3a – b equals to 11 or 1 and 3a + b equals to 1 or 11.
Let’s check both:
3a – b = 1 and 3a + b = 11
Solve the above system of equation:
a = 2 and b = 5
3a – b = 11 and 3a + b = 1
a = 2 and b = – 5
Since, a and b are positive integers, then, only a = 2 and b = 5 are the solutions.
Therefore, a – b = 2 – 5 = -3
The Best Books to Ace Algebra
Related to This Article
More math articles
- How to Decod Decimal Numbers: Dive into Place Values
- Other Topics Puzzle – Challenge 94
- The Ultimate GED Math Course [Updated for 2024]
- Best Calculators for the PSAT 10 Math Test
- 6th Grade STAAR Math Worksheets: FREE & Printable
- 6th Grade RICAS Math Worksheets: FREE & Printable
- How to Identify Characteristics of Quadratic Functions: Equations
- GRE Math Worksheets: FREE & Printable – Your Ultimate Preparation Tool!
- 10 Most Common 6th Grade Common Core Math Questions
- Number Properties Puzzle – Challenge 19
What people say about "Algebra Puzzle – Challenge 54 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.