SOLUTION: The product of two positive consecutive numbers is 42. What is the larger number?

Question 225878: The product of two positive consecutive numbers is 42. What is the larger number?
Found 2 solutions by Alan3354, drj:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
7

Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
The product of two positive consecutive numbers is 42. What is the larger number?

Step 1. Let n be the smaller positive number.

Step 2. Let n+1 be the next consecutive and larger positive number.

Step 3. Then n(n+1)=42 since their product is 42.

Step 4. Subtract 42 from both sides of the equation to get a quadratic.

Step 5. To solve, use the quadratic equation given below as

where a=1, b=1, and c=-42

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=169 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6, -7. Here's your graph:

Selecting the positive solution n=6, then n+1=7. Also note their product is 42.

Step 6. ANSWER: The larger number is 7.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

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