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

₹0.0

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

Options:

Correct Answer: 14 and 15

Exam Year: 2022

Solution:

Let the integers be n and n+1. Then n(n+1) = 240. Solving the quadratic equation n^2 + n - 240 = 0 gives n = 14, so the integers are 14 and 15.

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.

Consecutive Integers – Understanding the definition and properties of consecutive integers, which are integers that follow one another in order.
Quadratic Equations – Solving quadratic equations using factoring or the quadratic formula to find integer solutions.
Product of Integers – Applying the concept of multiplication to find the product of two numbers and setting up equations based on that product.