Step by step
The question
Question: The sum of four consecutive numbers is 90.
Find the numbers.
1 Find what we know
What do we know?
Consecutive means in a row.
Four numbers in a row, like 5, 6, 7, 8.
Each one is 1 more than the one before.
Added together, they make 90.
What do we want?
The 4 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.
The fourth number is 1 more again: x + 3.
3 Write the equation
In words: first plus second plus third plus fourth makes the sum.
So the equation is x + (x + 1) + (x + 2) + (x + 3) = 90.
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 + x = 4x.
1 + 2 + 3 = 6.
Now we have 4x + 6 = 90.
We want x by itself.
Two things are stuck to x: times 4 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 4.
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.
90 − 6 = 84.
Now we have 4x = 84.
7 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
84 divided by 4 is 21.
So x = 21!
8 Answer the question
The second number is x + 1: 21 + 1 = 22.
The third number is x + 2: 21 + 2 = 23.
The fourth number is x + 3: 21 + 3 = 24.
The numbers are 21, 22, 23 and 24.
9 Check
Let's check in the story.
Add the numbers: they make 90, like the story says.
And they are in a row, 1 apart.
Does it make sense?
90 shared by 4 is about 23.
Our numbers are close to 23.
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.