Step by step
The question
Question: Dan is 6 years younger than Eva.
The sum of their ages is 40.
How old is each?
1 Find what we know
What do we know?
Dan is 6 years younger than Eva.
Their two ages added together make 40.
What do we want?
How old each one is.
2 Name the unknown
We know Dan's age from Eva's age.
So we start with Eva.
We call Eva's age x.
Dan is 6 years younger.
Younger means less: x − 6.
3 Write the equation
In words: Eva's age plus Dan's age makes the sum.
So the equation is x + (x − 6) = 40.
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 − 6 = 40.
We want x by itself.
Two things are stuck to x: times 2 and − 6.
The − 6 is on the outside, so it comes off first.
Then the times 2.
6 Remove the − 6
To remove − 6, we add 6.
We do it on both sides, so they stay equal.
− 6 and + 6 make zero.
Cross them out.
40 + 6 = 46.
Now we have 2x = 46.
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.
46 divided by 2 is 23.
So x = 23!
8 Answer the question
Dan's age is x − 6: 23 − 6 = 17.
Eva is 23, Dan is 17.
9 Check
Let's check in the story.
Together: 23 + 17 = 40, like the story says.
And Dan is 6 years younger: the difference is 6.
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.