Step by step
The question
Question: Sara is 4 years older than Tom.
The sum of their ages is 30.
How old is each?
1 Find what we know
What do we know?
Sara is 4 years older than Tom.
Their two ages added together make 30.
What do we want?
How old each one is.
2 Name the unknown
We know Sara's age from Tom's age.
So we start with Tom.
We call Tom's age x.
Sara is 4 years older.
Older means more: x + 4.
3 Write the equation
In words: Tom's age plus Sara's age makes the sum.
So the equation is x + (x + 4) = 30.
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 + 4 = 30.
We want x by itself.
Two things are stuck to x: times 2 and + 4.
The + 4 is on the outside, so it comes off first.
Then the times 2.
6 Remove the + 4
To remove + 4, we take away 4.
We do it on both sides, so they stay equal.
+ 4 and − 4 make zero.
Cross them out.
30 − 4 = 26.
Now we have 2x = 26.
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.
26 divided by 2 is 13.
So x = 13!
8 Answer the question
Sara's age is x + 4: 13 + 4 = 17.
Tom is 13, Sara is 17.
9 Check
Let's check in the story.
Together: 13 + 17 = 30, like the story says.
And Sara is 4 years older: the difference is 4.
Does it make sense?
Ages are whole numbers, more than 0.
Ours are.
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.