Step by step
The question
Question: Mum is 32 and Ali is 8.
In how many years will Mum be 3 times as old as Ali?
1 Find what we know
What do we know?
Now Mum is 32 and Ali is 8.
What do we want?
In how many years Mum will be 3 times as old as Ali.
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.
Mum is 32 now.
Ali is 8 now.
In x years, everyone is x years older.
Mum: 32 + x.
Ali: 8 + x.
3 Write the equation
In words: Mum's age then is 3 times Ali's age then.
So the equation is 32 + x = 3(8 + x).
Now we solve it.
Careful: all of Ali's age, 8 + x, is 3 times.
So it goes in brackets.
4 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 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.
3x − x = 2x.
Now we have 32 = 24 + 2x.
Let's swap the two sides, so x is on the left.
We want x by itself.
Two things are stuck to x: times 2 and + 24.
The + 24 is on the outside, so it comes off first.
Then the times 2.
6 Remove the 24
To remove 24, we take away 24.
We do it on both sides, so they stay equal.
24 and − 24 make zero.
Cross them out.
32 − 24 = 8.
Now we have 2x = 8.
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.
8 divided by 2 is 4.
So x = 4!
8 Answer the question
Then Mum is 32 + 4 = 36.
And Ali is 8 + 4 = 12.
So in 4 years.
9 Check
Let's check in the story.
Mum will be 36 and Ali will be 12.
3 times 12 is 36, 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.