Step by step
The question
Question: The sum of three consecutive numbers is 50.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Three numbers in a row, like 5, 6, 7.
Each one is 1 more than the one before.
Added together, they make 50.
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 1 more: x + 1.
The third number is 1 more again: x + 2.
3 Write the equation
In words: first plus second plus third makes the sum.
So the equation is x + (x + 1) + (x + 2) = 50.
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.
1 + 2 = 3.
Now we have 3x + 3 = 50.
We want x by itself.
Two things are stuck to x: times 3 and + 3.
The + 3 is on the outside, so it comes off first.
Then the times 3.
6 Remove the + 3
To remove + 3, we take away 3.
We do it on both sides, so they stay equal.
+ 3 and − 3 make zero.
Cross them out.
50 − 3 = 47.
Now we have 3x = 47.
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.
So x = 47/3!
8 Answer the question
x = 47/3 is not a whole number.
But numbers in a row are whole numbers.
So there is no answer: no three numbers in a row add up to 50.
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Last: answer the question.