Step by step
The question
Question: A rectangle is 5 m longer than it is wide.
Its perimeter is 50 m.
Find the length and the width.
1 Find what we know
What do we know?
The length is 5 m more than the width.
The perimeter is 50 m.
Perimeter means all the way round.
What do we want?
The length and the width.
2 Name the unknown
We know the length from the width.
So we call the width x.
The length is 5 more: x + 5.
Let's draw it.
The long sides are x + 5.
The short sides are x.
3 Write the equation
All the way round: we add the four sides.
Width, length, width, length.
So the equation is x + (x + 5) + x + (x + 5) = 50.
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.
Plain numbers go together.
x + x + x + x = 4x.
5 + 5 = 10.
Now we have 4x + 10 = 50.
We want x by itself.
Two things are stuck to x: times 4 and + 10.
The + 10 is on the outside, so it comes off first.
Then the times 4.
6 Remove the + 10
To remove + 10, we take away 10.
We do it on both sides, so they stay equal.
+ 10 and − 10 make zero.
Cross them out.
50 − 10 = 40.
Now we have 4x = 40.
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.
40 divided by 4 is 10.
So x = 10!
8 Answer the question
The length is x + 5: 10 + 5 = 15.
So the width is 10 m and the length is 15 m.
9 Check
Let's check in the story.
All the way round: 10 + 15 + 10 + 15 = 50, like the story says.
And the length is 5 more than the width.
Does it make sense?
The length, 15 m, is longer than the width, 10 m.
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.