Step by step
The question
Question: A café sold 50 drinks.
Small drinks cost $2 and large drinks cost $3.
The café made $130.
How many of each drink were sold?
1 Find what we know
What do we know?
50 drinks in all.
Two kinds: small drinks cost $2 each, large drinks cost $3 each.
All the money: $130.
What do we want?
How many small drinks, and how many large drinks.
2 Name the unknown
We don't know how many small drinks.
So we call it x.
The rest are large.
50 in all, take away the x small ones: 50 − x.
For example: if 5 were small, then 50 − 5 = 45 would be large.
So we need only one letter.
Let's put it in a table: how many, the price, and the money.
Small: x drinks at $2 each.
Large: 50 − x drinks at $3 each.
Money = how many times the price.
2 times x is 2x.
3 times all of 50 − x is 3(50 − x).
We keep 50 − x together in brackets.
The total row: 50 drinks in all, and $130 in all.
3 Write the equation
In words: the small money plus the large money makes all the money.
So the equation is 2x + 3(50 − x) = 130.
Now we solve it.
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 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.
2x − 3x = −x.
Now we have −x + 150 = 130.
6 Remove the + 150
We want x by itself.
The + 150 is in the way.
To remove + 150, we take away 150.
We do it on both sides, so they stay equal.
+ 150 and − 150 make zero.
Cross them out.
130 − 150 = −20.
Now we have −x = −20.
7 Remove the −1
−x means −1 times x.
We want just x.
To remove times −1, we divide by −1.
We do it on both sides, so they stay equal.
−1 divided by −1 is 1.
So just x is left.
−20 divided by −1 is 20.
So x = 20!
8 Answer the question
Large: 50 − x.
50 − 20 = 30.
So 20 small drinks and 30 large drinks.
9 Check
Let's check in the story.
20 + 30 = 50 drinks, like the story says.
The money: $40 plus $90 makes $130, like the story says.
Does it make sense?
Both are whole numbers from 0 to 50.
That fits 50 drinks.
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.