Find 3 consecutive integers such that the sum of the first with twice the second and 3 times the third will give 80

Question

anonymous · Answer

The first step to figuring this out is probably but turning the sentences into equations.

We have 3 consecutive integers. So let's call the first one x. Then our 3 numbers are x, x+1, and x+2.

How can you write "the sum of the first with twice the second and 3 times the third gives 80" then?

anonymous · Answer

I got 

2nd number^2 - First number x 3rd number^3 = 80.

anonymous · Answer

Hmmm when it says "twice" and "3 times", you'll want to multiply by 2 and 3 instead of squaring and cubing. Squaring a number is not the same as twice the number. For example $$2*3 = 6$$ but $$3^2 = 9 $$

Why don't we take this step by step. Here's the sentence again:
the sum of the first with twice the second and 3 times the third gives 80

First, let's replace the words "first", "second", and "third" with our variable x:
the sum of x with twice (x+1) and 3 times (x+2) gives 80

Based on what I wrote at the top, how do you write "twice (x+1)" ?

anonymous · Answer

Ohhh, I see.. But why would we use the x variable when they are 3 different consecutive integers?

x + 1) squared? Since it is twice that number.

anonymous · Answer

Good question! We're using x to represent the first of our integers. Because they're consecutive, we know the second one is 1 greater than the first right? So we can write the second one as x+1. Similarly, the third one is one bigger than the second, or two greater than the first, so x+2! 

Actually,
$$(x+1)^2 = (x+1)(x+1) $$
which is (x+1) times (x+1), not 2 times (x+1). What does 2 times (x+1) look like?

anonymous · Answer

Oh o.O hmm (x + 1*2) which is inside the parenthesis.

anonymous · Answer

You're getting closer! 
(x+1*2) = x+2, which is the same as adding 1 to x+1.

Whenever you see the word "times" in a word problem, you want to switch out that word with a multiplication sign. So 2 times (x+1) = 2(x+1)! 

Does that make sense?

anonymous · Answer

Kind of :s Im sorry for the late reply, something came up. Ahh.

anonymous · Answer

That's alright!