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

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Question 225878: The product of two positive consecutive numbers is 42. What is the larger number?
Found 2 solutions by Alan3354, drj:
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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.