Step by step
The question
Question: Seeds cost $9 per kg and oats cost $3 per kg.
How many kg of oats must be mixed with 2 kg of seeds to make a mix that costs $5 per kg?
1 Find what we know
What do we know?
Seeds: $9 per kg.
Oats: $3 per kg.
We use 2 kg of seeds.
The mix costs $5 per kg.
What do we want?
How many kg of oats.
2 Name the unknown
We don't know how many kg of oats.
So we call it x.
The mix has both: x kg of oats and 2 kg of seeds.
So it is x + 2 kg.
Careful!
The mix has the oats too.
So it weighs x + 2 kg, not 2 kg.
Let's put it in a table: how much, the price, and the cost.
Oats: x kg at $3.
Seeds: 2 kg at $9.
Cost = how much times the price.
3 times x is 3x.
2 times 9 is $18.
The mix: x + 2 kg at $5.
Its cost is 5(x + 2): all of x + 2 is times 5.
3 Write the equation
In words: the oats cost plus the seeds cost makes the cost of the mix.
So the equation is 3x + 18 = 5(x + 2).
Now we solve it.
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 3x from the left side.
To remove 3x, we take away 3x.
We do it on both sides, so they stay equal.
3x and − 3x make zero.
Cross them out.
5x − 3x = 2x.
Now we have 18 = 2x + 10.
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 + 10.
The + 10 is on the outside, so it comes off first.
Then the times 2.
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.
18 − 10 = 8.
Now we have 2x = 8.
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.
8 divided by 2 is 4.
So x = 4!
8 Answer the question
So we need 4 kg of oats.
9 Check
Let's check in the story.
The cost: $12 plus $18 is $30.
The mix: 6 kg at $5 is $30.
The same cost, like the story says.
Does it make sense?
The mix costs between the two prices, $3 and $9.
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.