Step by step
The question
Question: Tea costs $10 per kg and mint costs $4 per kg.
How many kg of mint must be mixed with 3 kg of tea to make a mix that costs $6 per kg?
1 Find what we know
What do we know?
Tea: $10 per kg.
Mint: $4 per kg.
We use 3 kg of tea.
The mix costs $6 per kg.
What do we want?
How many kg of mint.
2 Name the unknown
We don't know how many kg of mint.
So we call it x.
The mix has both: x kg of mint and 3 kg of tea.
So it is x + 3 kg.
Careful!
The mix has the mint too.
So it weighs x + 3 kg, not 3 kg.
Let's put it in a table: how much, the price, and the cost.
Mint: x kg at $4.
Tea: 3 kg at $10.
Cost = how much times the price.
4 times x is 4x.
3 times 10 is $30.
The mix: x + 3 kg at $6.
Its cost is 6(x + 3): all of x + 3 is times 6.
3 Write the equation
In words: the mint cost plus the tea cost makes the cost of the mix.
So the equation is 4x + 30 = 6(x + 3).
Now we solve it.
4 Open the brackets
The 6 in front of the bracket multiplies every part inside.
So we write 6 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 4x from the left side.
To remove 4x, we take away 4x.
We do it on both sides, so they stay equal.
4x and − 4x make zero.
Cross them out.
6x − 4x = 2x.
Now we have 30 = 2x + 18.
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 + 18.
The + 18 is on the outside, so it comes off first.
Then the times 2.
6 Remove the + 18
To remove + 18, we take away 18.
We do it on both sides, so they stay equal.
+ 18 and − 18 make zero.
Cross them out.
30 − 18 = 12.
Now we have 2x = 12.
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.
12 divided by 2 is 6.
So x = 6!
8 Answer the question
So we need 6 kg of mint.
9 Check
Let's check in the story.
The cost: $24 plus $30 is $54.
The mix: 9 kg at $6 is $54.
The same cost, like the story says.
Does it make sense?
The mix costs between the two prices, $4 and $10.
That makes sense.
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.