Step by step
The question
Question: Big stamps cost $3 and small stamps cost $1.
Tara bought 4 more small stamps than big stamps.
She paid $24.
How many of each stamp did she buy?
1 Find what we know
What do we know?
Two kinds: big stamps cost $3 each, small stamps cost $1 each.
There are 4 more small stamps than big stamps.
All the money: $24.
What do we want?
How many big stamps, and how many small stamps.
2 Name the unknown
We know the small stamps from the big stamps.
So we start with the big stamps.
We call how many there are x.
4 more: x + 4.
Careful!
There are 4 more small stamps than big stamps.
So the + 4 goes with the small stamps, not the big stamps.
Let's put it in a table: how many, the price, and the money.
Big stamps: x of them, $3 each.
Small stamps: x + 4 of them, $1 each.
Money = how many times the price.
3 times x is 3x.
1 times all of x + 4 is 1(x + 4).
We keep x + 4 together in brackets.
The total: $24 in all.
3 Write the equation
In words: the big money plus the small money makes all the money.
So the equation is 3x + (x + 4) = 24.
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.
3x + x = 4x.
Now we have 4x + 4 = 24.
We want x by itself.
Two things are stuck to x: times 4 and + 4.
The + 4 is on the outside, so it comes off first.
Then the times 4.
6 Remove the + 4
To remove + 4, we take away 4.
We do it on both sides, so they stay equal.
+ 4 and − 4 make zero.
Cross them out.
24 − 4 = 20.
Now we have 4x = 20.
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.
20 divided by 4 is 5.
So x = 5!
8 Answer the question
Small stamps: x + 4.
5 + 4 = 9.
So 5 big stamps and 9 small stamps.
9 Check
Let's check in the story.
9 is 4 more than 5, like the story says.
The money: $15 plus $9 makes $24, like the story says.
Does it make sense?
Both are whole numbers, not below 0.
That fits stamps.
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.