Step by step
The question
Question: The sum of two consecutive numbers is 35.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Two numbers in a row, like 5, 6.
Each one is 1 more than the one before.
Added together, they make 35.
What do we want?
The 2 numbers.
2 Name the unknown
We don't know the first number.
So we call it x.
The second number is 1 more: x + 1.
3 Write the equation
In words: first plus second makes the sum.
So the equation is x + (x + 1) = 35.
Now we solve it.
4 Open the brackets
A bracket with a plus or nothing in front can just be removed.
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
x + x = 2x.
Now we have 2x + 1 = 35.
We want x by itself.
Two things are stuck to x: times 2 and + 1.
The + 1 is on the outside, so it comes off first.
Then the times 2.
6 Remove the + 1
To remove + 1, we take away 1.
We do it on both sides, so they stay equal.
+ 1 and − 1 make zero.
Cross them out.
35 − 1 = 34.
Now we have 2x = 34.
7 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
34 divided by 2 is 17.
So x = 17!
8 Answer the question
The second number is x + 1: 17 + 1 = 18.
The numbers are 17 and 18.
9 Check
Let's check in the story.
Add the numbers: they make 35, like the story says.
And they are in a row, 1 apart.
Does it make sense?
35 shared by 2 is about 18.
Our numbers are close to 18.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.