Step by step
The question
Question: A taxi charges $4 plus $3 per mile.
A ride costs $25.
How many miles was the ride?
There are four choices.
First we solve it, the normal way.
Then we pick.
1 Find what we know
What do we know?
$4 is paid one time.
$3 for each mile.
Altogether: $25.
What do we want?
How many miles.
2 Name the unknown
We don't know how many miles.
So we call it x.
3 Write the equation
In words: what the miles cost, plus the start, makes the total.
So the equation is 3x + 4 = 25.
Now we solve it.
We want x by itself.
Two things are stuck to x: times 3 and + 4.
First x was times 3.
Then + 4.
To take them off, we go backwards.
First we remove the + 4.
Then the times 3.
4 Remove the + 4
To remove + 4, we take away 4.
We do it on both sides, so they stay equal.
+ 4 and − 4 make zero.
Cross them out.
25 − 4 = 21.
Now we have 3x = 21.
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
21 divided by 3 is 7.
So x = 7.
6 Answer the question
So the answer is 7 miles.
7 Check
Let's check in the story.
7 miles at $3 each: 7 times 3 is $21.
Plus the $4 at the start: $25, like the story says.
Does it make sense?
A whole number of miles.
And the total, $25, is more than the $4 start.
So the answer is right!
8 Pick the choice
Our answer is 7 miles.
That is choice A.
9 Why not the others
B is 25/3.
Wrong: 25 ÷ 3: forgot the $4.
C is 29/3.
Wrong: added 4: 29 ÷ 3.
D is 21.
Wrong: 3x = 21, but we still had to divide by 3.
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.