ASVAB Math Practice — Mixed Problem Set Step by Step | Coach Anderson

[00:00:02]All right, so starting this next one up everybody. What we're always going to begin with first is reading the question sentence first. So, what we're going to do here is we start where it asks what is the length? So, my party people, here it is very very very easy to go ahead and go through a problem without fully understanding what the numbers mean. And this is going to be a good example of that. So, here what we have is if the length is 19 ft, what is the width?

[00:00:35]Okay, sounds good. So, length is 19, what is the width? And you can clearly tell here that we're given a length, we're asking for the width.

[00:00:47]It's very possible we're dealing with a shape here.

[00:00:50]So, what shape might that be? Well, let's go ahead and just take a look here. It says a rectangular patio.

[00:00:56]So, a rectangular patio uses 56 ft of border material to go around it completely.

[00:01:01]Here's the length, what's the width? But this is the information that's really going to get us hung up. Right here. 56 ft of border material to go around it.

[00:01:16]That's the key there everybody.

[00:01:18]56 ft of border material to go around it.

[00:01:23]So, now that we're here and thinking about that, what does going around a shape really mean?

[00:01:31]Think about that. When it comes to geometry and word problems, going around a shape, that's perimeter.

[00:01:39]That is perimeter all day. And so, that's what we're given. The 56 ft of material going around, that is going to be all day the perimeter.

[00:01:57]So, what are we going to do with that, everybody? What we're going to do with that is we're going to go ahead and notice that we have a rectangle, we have perimeter, and we're going to write out our formula. That formula is perimeter equals double the length plus double the width. And so, all this together, we're now going to go ahead and plug in the values we have so we can find the value we don't.

[00:02:23]So, the 56, that is perimeter. Let's go ahead and plug that in safely.

[00:02:30]And then from there, we have double the length. The length was given to us as 19 ft.

[00:02:36]So, I'll say double 19.

[00:02:40]And we're looking for the width, so I'll keep that as is.

[00:02:43]So, let's go ahead and finish things up.

[00:02:46]We'll go ahead and multiply two and the 19 together, and that'll end up being 38.

[00:02:51]So, we have 38 + 2 W, and then 56 on the left side, right there.

[00:02:58]Then from here, what we need to do is we need to continue trying to get that W by itself.

[00:03:03]So, we have double right here * 2, and we also have + 38.

[00:03:08]I'm going to get rid of the 38 first.

[00:03:10]If it helps you see it any better, 2 W + 38 is the same as 38 + 2 W. So, if you needed to go ahead and kind of move this in this way, that works. That is absolutely fine. So, from here, my party people, let's go ahead and subtract the 38 from both sides that we can see.

[00:03:34]From there and there, cancels out on the right side, and on the left side, we have 56 - 38. And what we'll get from that will be what?

[00:03:44]Well, we'll have to borrow a little bit here to make that four and 16. 16 - 8 is 8. 4 - 3 is 1. So, what we have here is double the width is 18.

[00:03:56]One last step is to divide both sides by two, right here on the right and on the left. And once we have that going on, perfect, we're good. And we will have the width equals nine. 9 ft for our width, and there's our correct answer, answer choice C.

[00:04:18]All right. So, my party people, starting up right here, as always, just understand what's going on working forward. So, here we have 4x = -376.

[00:04:29]So, I know that we're looking at a negative. I know that it doesn't look the prettiest, but all we should really be focusing on them and asking ourselves, everyone, is this.

[00:04:39]What operation is happening between the four and the X? What operation are we currently looking at?

[00:04:49]Yeah, we're currently seeing, we're witnessing multiplication. 4x, four next together, that is multiplication. So, all you need to do from here is the opposite operation. Instead of multiplying by four, we will divide by four on both sides. Nice and easy.

[00:05:09]Getting you X by itself.

[00:05:11]And now what you have on your hands is 376 / 4, and just don't forget that negative.

[00:05:17]Because you might notice two answers here are pretty similar, but it might depend on your confidence with negatives, right? So, let's go ahead and first show that long division, 376 / 4.

[00:05:30]First, I'll show it to you with my broken handwriting, just like just like this, and then I'll show you with a little tool that I created in case anybody wants to see it a little more clearly.

[00:05:39]So, we have four going into three, it doesn't.

[00:05:42]But then we ask, how many times does four go into 37?

[00:05:46]That's going to be nine times, because 9 * 4 is 36.

[00:05:51]When we subtract that, we have one left over.

[00:05:54]And then from there, we'll drop that six.

[00:05:56]And so then we have four going into 16, which would be four times.

[00:06:01]So it's again very easy to get tempted to pick the wrong answer here, because you might get pretty excited about doing the division, getting 94, but then completely forgetting about the negative.

[00:06:13]My party people, just remind me, when we have a negative value divided by a positive one, the result will be what?

[00:06:22]Yeah, it's going to be negative.

[00:06:24]A negative divided by a positive will be negative. And so it'll still be 94, just negative 94. And that's why the correct answer here will be answer choice B.

[00:06:38]Just like that. And so I want you to remember that a lot of the times, your success, not in every part of the problem, but your success might depend on remembering one and very important rule right at a specific point like the very very end of the problem.

[00:06:56]All right, let's take care of one more here. So what we're being asked to do is what is the slope of the line shown on this graph?

[00:07:05]All right.

[00:07:06]So if we're trying to find the slope of a line everybody, here's how we do it.

[00:07:10]You're going to grab two solid points.

[00:07:13]And once you have those two solid points, you're going to figure out what the rise over run is going to be.

[00:07:21]So first and foremost, everybody, quick question.

[00:07:23]What is the slope of this line? Is it positive, negative, or zero?

[00:07:28]You tell me.

[00:07:32]Yeah, this one's positive. If you take a look, as we go left to right, we're increasing. We're increasing, so this is a positive slope. So if you're nervous about this one, there's no way A can be an answer.

[00:07:45]That's a negative. So, no way that could be it. And now I'm going to choose my two solid points. I'm going to choose let's go ahead and say looks like that'll be a good point, that's a good point, that's a good point. It looks like every X value is a good point. And if I just take a look here, moving over one, you're going up twice.

[00:08:06]Up two over one. Up two over one. Yeah, so I have my rise over run. My rise is two. I go up two for every time that I go over one. And my party people, 2 / 1 that's just two.

[00:08:21]The correct answer here is answer choice C.

[00:08:26]And we're all good.

[00:08:29]So, to get this problem solved everybody, we're taking a look at -5x is less than 15. And so, as a reminder, inequalities, just like equations, we're just working backwards. And we just have to pay attention to the symbol whenever we multiply or divide both sides by a negative.

[00:08:47]Fortunately, that exact example is about to happen now, where we divide both sides by -5.

[00:08:55]And what happens is, yeah, sure that a cancellation happens.

[00:08:58]But because we negated both sides, we have to negate the symbol. So, instead of it saying less than, it will be greater than. So, that's number one.

[00:09:10]And then number two everybody, we have to remember when we divide a positive by a negative, it is going to be a negative result. And then 15 / 5, that's going to give us three.

[00:09:23]Just like that. And so, there's our answer. Our answer is X is greater than -3. Which answer shows that? Greater than -3, it's this one right here.

[00:09:34]Answer choice B.