### Video Transcript

Today, let’s look at writing
equations and then solving them mentally. But before we start trying to write
equations, we probably should ask the question, what is an equation? An equation is a sentence that
contains two expressions separated by an equal sign. Here’s an example of that. Seven equals eight minus one. Here’s another example. 18 equals 13 plus 𝑥. This equation contains a variable
which is the 𝑥. This equation, 18 equals 13 plus
𝑥, is neither true or false until the variable is replaced with a number.

Let’s say we replaced 𝑥 with a
three. The equation is now false because
18 is not equal to 16. But when we’ve replaced the 𝑥 with
the five, it becomes a true statement. We say that the equation here is
true when 𝑥 equals five. We also say that five is the
solution of the equation. A solution of an equation is the
numerical value for the variable that makes the sentence true. In this case, five makes our
sentence true. Solving an equation is the process
of finding a solution. When we try to figure out what the
variable is equal to, we call that solving the equation. Now, let’s take a look at how we
solve an equation with mental math.

So here’s an equation. 𝑝 minus five equals 20.

Remember that we wanna solve these
problems mentally without writing things down. So we think some number take away
five is equal to 20. And that number must be five more
than 20. Therefore, 𝑝 must equal 25. 𝑝 equals 25 is the correct
answer.

Here’s another example. If 𝑘 equals 60, is 28 plus 26
equal 𝑘 true or false?

And again we wanna use a mental
math strategy to solve this question. So you think about 28 and 26. They have an eight and a six in
their ones position. And 60 has a zero in its one
position. Eight plus six equals 14. And that means the solution to 𝑘
is going to have to have a four in the ones position. At this point, we don’t know what
𝑘 is. But we know that if 𝑘 equals 60,
then this sentence must be false. We can say for sure that 28 plus 26
does not equal 60, which makes this statement false. Now, we are going to look at a
question that asks us to write an equation.

The total cost of a skateboard and
knee pads is 247 dollars. If the skateboard costs 235
dollars, write an equation to find the cost of the kneepads, 𝑘. Then solve the equation.

The problem is asking us to do two
things, write an equation and then solve the equation that we write. We’re given three different pieces
of information. The total cost is 247 dollars. The skateboard costs 235
dollars. And the missing cost, the cost that
we don’t know, is 𝑘, and that’s the cost of the kneepads. We know that the total cost equals
the skateboard price plus the kneepads price. Let’s substitute these two pieces
with the information that we already know. Total cost is 247. Skateboard costs 235. What should we put here for the
knee pads price? Because we don’t know the knee pads
price, we need to substitute a variable here. In our case, that’s where the 𝑘
goes. Our equation becomes 247 equals 235
plus 𝑘.

Step one of the problem is
complete. This is an equation we can use to
solve step two. And this part can be done
mentally. What added to 235 would equal
247? Well, if you add ten, you get from
235 to 245 add two more to that and now you’re at 247. Put both of those numbers you added
together, 10 and two, and you realise that 𝑘 must be equal to 12. 𝑘 is equal to twelve. And that means the kneepads cost 12
dollars. Our final answer here is 𝑘 equals
12 dollars.