On the TEAS test, you are going to encounter a lot of word problems. Here we have one example

of something you might see when taking the TEAS test. It says, "If Sara can read fifteen

pages in ten minutes, how long will it take her to read forty-five pages?" Here we have

a rate: fifteen pages in ten minutes. Which can be written as a ratio, or a fraction.

Fifteen pages in ten minutes. Or, you can write it in the reverse: ten minutes in fifteen

pages, or ten minutes to fifteen pages. Then we have this third piece of information: forty-five

pages. And you see that the units there, the pages, match the units, or one of the units

you have in your first ratio. That needs to be a clue to use a proportion, which is just

a ratio that's equal to a ratio. And what's really important about setting up proportions,

is that you're consistent. So if your first ratio is pages to minutes, then your second

ratio should also be pages to minutes, which tells us to put the forty-five pages on top

of our fraction in our numerator. So what were trying to find is, how many minutes is

it going to take to read those forty-five pages. There is more than one way to solve

a proportion. One of the easier ways, and it won't always work because the easier ways

don't always work or we wouldn't come up with the harder ways. One of the easier ways to

solve this would be: to look at either the numerator or the denominator, and figure out

what you'd have to do to get your other numerator. For example, what do you have to do to fifteen

pages to get forty-five pages? Well fifteen times three is forty-five. So you just do

the same thing in your denominator. Ten times three would be thirty minutes. So it's going

to take thirty minutes to read those forty-five pages. But like I said, that won't always

work. What will always work, is using cross-products. And that just means cross-multiplying. Fifteen

times "x" is "15x". And that is equal to ten times forty-five, which is four hundred fifty.

What you need to know about proportions is that, their cross products are always equal.

So now you just need to solve your equation, which means undoing what's been done to your

variable "x". So in this case, we need to divide both sides by fifteen. And "x", again

equals thirty. So now we know it's going to take thirty minutes to read those forty-five

pages. On the TEAS test, you're going to see a lot

of word problems. Here is one example of one type of word problem that you might see, "Restaurant

customers tip their server only eight percent for poor service. If their tip was three dollars

and seventy cents, how much was their bill?" So here we have a percent, the tip, or part,

that's part of a whole, and then what we're asked to find is the whole. So you can use

the percent equation, that part is equal to percent times whole to solve this problem.

Your part, in this case, is the tip. The tip they left was three dollars and seventy cents.

The percent is this eight percent, but we don't do calculations with percents. So you

have to either, change that percent into a decimal or into a fraction. Eight percent,

as a decimal, is eight hundredths. The way you go from a percent to a decimal is: just

to take the decimal in eight percent, which is at the back of the number, and move it

two places to the left and then filling that empty place with a zero. So for this percent,

we put our eight hundredths times the whole, and the whole is what we're trying to find.

So that is our variable "x". Now to solve for "x", you just need to undo multiplying

"x" by eight hundredths by dividing both sides by eight hundredths. Three dollars and seventy

cents divided by eight hundredths is forty six dollars and twenty-five cents, which means

that, the bill for their meal was forty six dollars and twenty-five cents. So there is

one example of a problem that you might see on the TEAS test.

On the TEAS test, you're going to see a lot of word problems. Here I have one example

of a word problem that you might encounter on the TEAS test. "If Leonard bought two packs

of batteries for 'x' amount of dollars, how many packs of batteries could he purchase

for five dollars at the same rate?" This is a key word right here, rate, because it tells

you to set up a ratio, or a proportion actually. So our first rate that we have is two packs

of batteries for "x" dollars. We can set that up as two packs for "x" dollars. And then

it says "at the same rate", which tells us we're going to set up a proportion. The key

with proportions is to be consistent. Looking at our first ratio, we have packs to dollars.

So our second ratio should also be packs to dollars. And the information they've given

us is the five dollars, which goes in your denominator with dollars. What we don't know

is how many packs of batteries. That's what we're trying to figure out, "...how many packs

of batteries could he purchase..." So I'm going to us "y", since we already used "x"

down here. What we have to keep in mind since we have two different variables is that: were

trying to solve for "y" this time, not for "x". Notice, in our multiple-choice answers,

that they all have that variable "x" in it. So we're trying to solve for "y" this time,

not "x", which is kind of weird. Just having two variables is kind of weird. Okay, so to

solve this proportion and to solve any proportion, we can use cross-products, which just means

cross-multiply. Two times five is ten, and that's equal to "x" times "y". Again, we have

to remember that we're trying to solve for "y", not for "x". "X" is actually part of

our answer. In order to get "y" alone, we need to undo multiplying by "x" by dividing

by "x". So, "y" or the number of packs of batteries that Leonard can buy, is ten divided

by "x". So there you have an example of a problem that you may encounter when you take

the TEAS test. The TEAS test has a lot of word problems on

it. Here is one example of a type of word problem that you could encounter when you

take the TEAS test. It says, "Choose the algebraic expression that best represents the following

situation: Jeral's score, 'j', was five points higher than half of Kara's test score 'k'".

I like to say that we're taking English and translating it into "math" in this case. So,

if you can figure out what the key words mean, then this is, actually, pretty simple. So

we're just starting with "j". This word "was" is the past tense of "is". "Is" in math means

equals. So this word "was" is an equals sign. And of course, five is five. "Higher than"

tells you to add. It's just like more than or greater than, and all those words mean

"to add". Half, of course, means half. "Of" is another really important word. "Of" tells

you to multiply. So, you multiply whatever comes on either side of the word "of". So,

it's half times Kara's test score "k". So it's half "k". Another thing with higher than,

or greater than, or more than, is that word "than" tells you that, actually, you need

to switch the order. In stead of writing five plus half "k", you just switch these around.

So it says "j" equals half "k" plus five. But really, these say the same thing, since

when you're adding, it doesn't matter the order that you add two things in, you get

the same answer. That's the commutative property of addition. So, um, we see then that "a"

is our answer here. And there you have one example of a type of word problem that you

may encounter when you take the TEAS test. You're going to encounter a lot of word problems

on the TEAS test. So, let me walk you through how to solve one type of word problem you

may encounter. "Enrique weighs five pounds more than twice Brendon's weight. If their

total weight is two hundred twenty-five pounds, how much does Enrique weigh?" Even though

this is a short problem, there are, actually, two different equations we can write from

it. The first one starts with the first sentence. "Enrique weighs..." this is another way of

saying "Enrique is", and "is" in math is an equal sign. Since we don't know Enrique's

weight, we'll use a variable. In this case, an "e" makes sense. So, "Enrique is five pounds

more than...", and more than tells us to add, "...twice Brendon's weight." We also don't

know Brendon's weight. So, we need another variable, and in this case, a "b" would make

sense. The "twice" tells us to multiply times two. So, since it's twice Brendon's this is

actually going to be two times "b". "...more than...", besides telling us to add, also

tells us to switch around the order. So, instead of writing five plus "2b" we would write "2b"

plus five. Now, honestly, it doesn't really matter, five plus "2b", "2b" plus five, it

is the same thing. That's the commutative property of addition. That's the first sentence

and our first equation. Our second sentence has our second equation. "If their total weight

is two hundred twenty-five pounds, how much does Enrique weigh?" "Total" tells you to

add. And what are we adding? Enrique and Brendon's weight together. So, Enrique's weight plus

Brendon's weight is, and again that "is" tells us that it's an equal sign, two hundred twenty-five.

Okay so, how are we supposed to solve these two equations, that each have two different

variables? Well you have several options: you could graph both of these equations, which

I know nobody wants to do. You could use elimination, but really they're not set up for that. This

one is, but this one isn't because the "2b" isn't on the same side. Like this equation

you have both variables on the same side of the equal sign, but you don't in this one.

So, what they're really set up to is substitution. And, since that's the easiest way to solve

it, I think that makes the most sense. We're going to use substitution. We're going to

take this "2b plus five" and use it to replace the "e" in this equation. Since, what this

says is that "e" and "2b plus 5" are the same thing, then we can replace the "e" with this

expression "2b plus five". This equation then becomes: "2b plus 5", instead of the "e",

plus "b" equals two hundred twenty-five. Now we're able to actually solve this equation,

because it only has one variable. Starting with combining your like terms of "2b" plus

another "b" which is a total of "3b"s plus five equals two hundred twenty-five. Now we

need to subtract five from both sides. "3b" is equal to two hundred twenty, and then divide

both sides by three. So two hundred twenty divided by three is not a pretty number. Three

goes into twenty-two seven times, that'd be twenty-one. One left over, ten, three. So,

it's seventy-three and actually three-tenths repeating, or you could say seventy-three

and one third. Okay, but going back to the question, they didn't ask us how much Brendon

weighed, they asked us how much Enrique weighed. So, now that we know Brendon's weight, we

can use that to find Enrique's weight, by using this equation that already says, Enrique

what does he weigh? He weighs twice Brendon's weight, which we just found is seventy-three

and three-tenths repeating or seventy-three and one-third plus five. So, Enrique weighs

two times seventy-three and one-third, is one hundred forty-six and two-thirds plus

five. So, that is one hundred fifty-one and two-thirds, which is closest to the one hundred

fifty-two pounds. So, there you have an example of a type of word problem that you may encounter

when you take the TEAS test.