The product of two consecutive integers is 240. What are the integers? (2022)

The product of two consecutive integers is 240. What are the integers? (2022)

Step 1: Understand that consecutive integers are numbers that follow one after the other, like 14 and 15.
Step 2: Let the first integer be represented as 'n'. Then the next consecutive integer can be represented as 'n + 1'.
Step 3: Write an equation for the product of these two integers: n * (n + 1) = 240.
Step 4: Expand the equation: n^2 + n = 240.
Step 5: Rearrange the equation to set it to zero: n^2 + n - 240 = 0.
Step 6: Solve the quadratic equation using the quadratic formula or factoring. In this case, we can factor it as (n - 14)(n + 15) = 0.
Step 7: Set each factor to zero: n - 14 = 0 or n + 15 = 0.
Step 8: Solve for n: From n - 14 = 0, we get n = 14. The other factor gives a negative integer, which we don't need.
Step 9: Find the consecutive integers: If n = 14, then the next integer is n + 1 = 15.
Step 10: Conclude that the two consecutive integers are 14 and 15.

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