[MUSIC] Let's look at solving linear word problems.

[SOUND] A total of 703 tickets were sold for the school play.

They were either adult or student tickets.

There were 53 more student tickets sold than adult tickets.

How many adult tickets were sold? Let's start by introducing some notations

here. Let's let s be equal to the number of

student tickets sold and a be equal to the number of adult tickets sold.

Now, we're told that there were 53 more student tickets sold than adult tickets.

That is, s, which is the number of student tickets sold is equals to a,

which is the number of adult tickets sold, plus 53.

There's 53 more student tickets sold. Moreover, the total number of tickets

sold was 703. And since they are either adult tickets

or student tickets, that means that s + a has to equal 703.

Now, we're asked to find out how many adult tickets were sold which means we

want to solve for a. Therefore, if we replace in this

equation, s with a + 53, then we'll have an equation that just involves a and

we'll be able to solve for it. So, let's do that.

That is we have a + 53 + a = 703. And then, combining like terms on the

left, gives us 2a + 53 = 703. And now, we can subtract 53 from both

sides, which gives us, 2a = 703 - 53 or 2a = 650, and then dividing both sides by

2 gives us a = 325. So, there were 325 adult tickets sold to

this play. Alright,

let's look at another example. [SOUND] James will rent a car for the

weekend. He can choose one of two plans.

The first plan has an initial fee of $69 and costs an additional $0.60 for every

mile driven. Whereas, the second plan has no initial

fee but costs $0.90 for every mile driven.

How many miles would James need to drive for the two plans to cost the same? Well,

let's let x equal the number of miles that James drives.

What then would be the cost of the first plan? Well, he has to pay an initial fee

of $69 and then an additional $0.60 for every mile driven.

That is, this is equal to 69 + 0.60 * x, because x is the number of miles that

he's going to drive and for every one of those miles, the'y're going to charge him

another $0.60. Now, what about the cost of the second

plan? Now, there's no initial fee but it's going to cost him $0.90 for every

mile driven. That is, this is equal to 0.90 * x.

Now, we want to know how many miles he would need to drive for the two plans to

cost the same. So, we want to find the value of x that

will make these equal. That is, we'll solve the following

equation for x. 69 + 0.60x = 0.90x, or 69 = 0.90x -

0.60x, or Or 69 = 0.30 * x and now we can divide

both sides by 0.30, which gives us But 0.30 is 3 / 10, so this is equal to 69 *

10 / 3. And 3 goes into 69, 23 times.

Therefore, this is equal to 23 times 10 or 230.

Therefore, the answer to our question here is 230 miles.

And this is how we solve these types of linear word problems.

Thank you and we'll see you next time. [MUSIC]