Step by step
The question
Question: The sum of three consecutive odd numbers is 51.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Three odd numbers in a row, like 7, 9, 11.
Each one is 2 more than the one before.
Added together, they make 51.
What do we want?
The 3 numbers.
2 Name the unknown
We don't know the first number.
So we call it x.
The second number is 2 more: x + 2.
Careful: odd numbers in a row also go up by 2, not 1.
Like 7, 9, 11.
The third number is 2 more again: x + 4.
3 Write the equation
In words: first plus second plus third makes the sum.
So the equation is x + (x + 2) + (x + 4) = 51.
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.
Plain numbers go together.
x + x + x = 3x.
2 + 4 = 6.
Now we have 3x + 6 = 51.
We want x by itself.
Two things are stuck to x: times 3 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 3.
6 Remove the + 6
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
+ 6 and − 6 make zero.
Cross them out.
51 − 6 = 45.
Now we have 3x = 45.
7 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
45 divided by 3 is 15.
So x = 15!
8 Answer the question
The second number is x + 2: 15 + 2 = 17.
The third number is x + 4: 15 + 4 = 19.
The numbers are 15, 17 and 19.
9 Check
Let's check in the story.
Add the numbers: they make 51, like the story says.
And they are odd numbers in a row, 2 apart.
Does it make sense?
51 shared by 3 is 17.
Our numbers are close to 17.
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.