# Writing and Solving Equations

The product of 2 consecutive positive integers is 398 more than the next integer. What is the largest of the 3 integers?

### Comments for Writing and Solving Equations

Average Rating     Jan 27, 2010 Rating     Writing and Solving Equations by: Karin Great Problem! I love it. You need to ask yourself, what do I know in the problem and what do I need to find out? You need to find the 3 integers and you know that the integers are consecutive. So, let's define our variable. Let x = the first integer If x is the first integer than x + 1 is the next integer. x + 2 would be the third integer. So, we are working with x, x + 1, and x + 2 The problem says that the product of the first two integers is ..... Product means multiply, so I am going to multiply my first two integers: x(x+1) = Now, the answer: "is 398 more than the next integer". x(x+1) = x+2+398 (The next integer is x + 2 and it's 398 more than that) So, our equation that we need to solve is: x(x+1) - x+ 2 + 398 x2 + x = x + 400 x2 + x - x = x - x = 400 x2 = 400 Take the square root of both sides: x = 20 So, the three integers are 20, 21, 22. The largest of the three is 22. Check your answer: 20 * 21 = 420 22+398 = 420 You just need to break your word problems down into small parts and write the equation. Then work on solving the equation. I hope this helps! All the best, Karin