Step by step
The question
Question: Dad is 40 and Sam is 10.
In how many years will Dad be twice as old as Sam?
1 Find what we know
What do we know?
Now Dad is 40 and Sam is 10.
What do we want?
In how many years Dad will be 2 times as old as Sam.
2 Name the unknown
We don't know how many years.
So we call it x.
Let's put the ages in a table: now, and in x years.
Dad is 40 now.
Sam is 10 now.
In x years, everyone is x years older.
Dad: 40 + x.
Sam: 10 + x.
3 Write the equation
In words: Dad's age then is 2 times Sam's age then.
So the equation is 40 + x = 2(10 + x).
Now we solve it.
Careful: all of Sam's age, 10 + x, is 2 times.
So it goes in brackets.
4 Open the brackets
The 2 in front of the bracket multiplies every part inside.
So we write 2 times each part.
Work out each multiplication.
5 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the x from the left side.
To remove x, we take away x.
We do it on both sides, so they stay equal.
+ x and − x make zero.
Cross them out.
2x − x = x.
Now we have 40 = 20 + x.
Let's swap the two sides, so x is on the left.
6 Remove the 20
We want x by itself.
The 20 is in the way.
To remove 20, we take away 20.
We do it on both sides, so they stay equal.
20 and − 20 make zero.
Cross them out.
40 − 20 = 20.
So x = 20!
7 Answer the question
Then Dad is 40 + 20 = 60.
And Sam is 10 + 20 = 30.
So in 20 years.
8 Check
Let's check in the story.
Dad will be 60 and Sam will be 30.
2 times 30 is 60, like the story says.
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.