Step by step
The question
Question: Shop A charges $24 plus $6 per box.
Shop B charges $10 per box.
After how many boxes do the two shops cost the same?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find what we know
What do we know?
Shop A: $24 one time, plus $6 for each box.
Shop B: $10 for each box.
What do we want?
How many boxes make the two costs the same.
2 Name the unknown
We don't know how many boxes.
So we call it x.
Shop A: $6 for each box, so x boxes cost 6x.
Plus $24 one time: 6x + 24.
Shop B: $10 for each box, so x boxes cost 10x.
3 Write the equation
In words: Shop A's cost is the same as Shop B's cost.
So the equation is 6x + 24 = 10x.
Now we solve it.
4 Get x on one side
There is x on both sides.
We want x on one side only.
The numbers in front of x are 6 and 10.
We remove the smaller one, 6x, so the x part that is left is plus.
So we remove the 6x from the left side.
To remove 6x, we take away 6x.
We do it on both sides, so they stay equal.
6x and − 6x cancel each other.
They make zero.
10x − 6x = 4x.
Now we have 24 = 4x.
Let's swap the two sides, so x is on the left.
Both sides are the same amount, so we can swap them.
So after step 4: we took away 6x, and now we have 4x = 24.
Is x alone now?
Not yet: 4x means 4 times x.
How do we remove it?
5 Remove the 4
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
They cancel each other.
So just x is left.
24 divided by 4 is 6.
So x = 6.
6 Answer the question
So after 6 boxes, they cost the same.
7 Check
Let's check in the story.
Shop A: $24 + 6 × $6 = $60.
Shop B: 6 × $10 = $60.
The same cost, like the story says.
Check it with the picture.
Shop A: $60.
Shop B: $60.
The same.
So the answer is right!
8 Pick the choice
Our answer is 6 boxes.
That is choice B.
9 Why not the others
A is 4.
Wrong: 24 ÷ 6: left out Shop B.
C is 12.
Wrong: 24 ÷ 2: the difference per box is 10 − 6 = 4.
D is 24.
Wrong: that is Shop A's start, not a number of boxes.
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.