The product of two consecutive positive integers is 23 more than the next integer. What is the largest of the three integers?

Question

I have no additional details about my question. 

Answer 1

a) Define the 3 integers in order as x, x+1, x+2.

b) Set up the relationship between all 3 integers:

x*(x+1) = (x+2) + 23

c) Solve the equation

X*X + X*1 = X + 25

X^2 + X - X = 25

X^2 = 25

X = 5

d) Substitute X to answer the original question.

5, 5+1, 5+2, so integers are 5,6,7. The largest of the 3 integers is 7.

Answer 2

In this problem we have a couple of variables that we need to figure out and we will be doing so with a system of equations.

We have three integers that we will call I₁,I₂, and I₃.

I₁ is the smallest and I₃ is the largest.

 

From the fact that they are three consecutive integers we have:

 

I₁+1 = I₂

I₂+1 = I₃

 

We also have the statement that the product of I₁ and I₂ is 23 more than I₃. This translates into this equation:

 

I₁ * I₂ = I₃ + 23

 

Now we have three equations and three unknowns so you can solve the system of equations with substitution.

 

I'll leave the substitution to you as I don't want to do the problem for you, but if you still have trouble let me know.

 

Good luck!