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?

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Jan 27, 2010
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,

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