Step by step
The question
Question: Cashews cost $14 per kg and peanuts cost $4 per kg.
How many kg of cashews must be mixed with 6 kg of peanuts to make a mix that costs $9 per kg?
1 Find what we know
What do we know?
Cashews: $14 per kg.
Peanuts: $4 per kg.
We use 6 kg of peanuts.
The mix costs $9 per kg.
What do we want?
How many kg of cashews.
2 Name the unknown
We don't know how many kg of cashews.
So we call it x.
The mix has both: x kg of cashews and 6 kg of peanuts.
So it is x + 6 kg.
Careful!
The mix has the cashews too.
So it weighs x + 6 kg, not 6 kg.
Let's put it in a table: how much, the price, and the cost.
Cashews: x kg at $14.
Peanuts: 6 kg at $4.
Cost = how much times the price.
14 times x is 14x.
6 times 4 is $24.
The mix: x + 6 kg at $9.
Its cost is 9(x + 6): all of x + 6 is times 9.
3 Write the equation
In words: the cashews cost plus the peanuts cost makes the cost of the mix.
So the equation is 14x + 24 = 9(x + 6).
Now we solve it.
4 Open the brackets
The 9 in front of the bracket multiplies every part inside.
So we write 9 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 9x from the right side.
To remove 9x, we take away 9x.
We do it on both sides, so they stay equal.
9x and − 9x make zero.
Cross them out.
14x − 9x = 5x.
Now we have 5x + 24 = 54.
We want x by itself.
Two things are stuck to x: times 5 and + 24.
The + 24 is on the outside, so it comes off first.
Then the times 5.
6 Remove the + 24
To remove + 24, we take away 24.
We do it on both sides, so they stay equal.
+ 24 and − 24 make zero.
Cross them out.
54 − 24 = 30.
Now we have 5x = 30.
7 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
30 divided by 5 is 6.
So x = 6!
8 Answer the question
So we need 6 kg of cashews.
9 Check
Let's check in the story.
The cost: $84 plus $24 is $108.
The mix: 12 kg at $9 is $108.
The same cost, like the story says.
Does it make sense?
The mix costs between the two prices, $4 and $14.
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.