Step by step
The question
Question: Mum is 34 and Leo is 10.
How many years ago was Mum 5 times as old as Leo?
1 Find what we know
What do we know?
Now Mum is 34 and Leo is 10.
What do we want?
How many years ago Mum was 5 times as old as Leo.
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 x years ago.
Mum is 34 now.
Leo is 10 now.
x years ago, everyone was x years younger.
Mum: 34 − x.
Leo: 10 − x.
3 Write the equation
In words: Mum's age then is 5 times Leo's age then.
So the equation is 34 − x = 5(10 − x).
Now we solve it.
Careful: all of Leo's age, 10 − x, is 5 times.
So it goes in brackets.
4 Open the brackets
The 5 in front of the bracket multiplies every part inside.
So we write 5 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 −5x from the right side.
To remove −5x, we add 5x.
We do it on both sides, so they stay equal.
− 5x and + 5x make zero.
Cross them out.
−x + 5x = 4x.
Now we have 34 + 4x = 50.
We want x by itself.
Two things are stuck to x: times 4 and + 34.
The + 34 is on the outside, so it comes off first.
Then the times 4.
6 Remove the 34
To remove 34, we take away 34.
We do it on both sides, so they stay equal.
34 and − 34 make zero.
Cross them out.
50 − 34 = 16.
Now we have 4x = 16.
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.
16 divided by 4 is 4.
So x = 4!
8 Answer the question
Then Mum is 34 − 4 = 30.
And Leo is 10 − 4 = 6.
So 4 years ago.
9 Check
Let's check in the story.
Mum was 30 and Leo was 6.
5 times 6 is 30, 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.