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We're on problem 87. Machine A produces parts twice as fast as machine B does. So machine A produces 100 parts twice as fast as machine B, let me just keep reading, machine B produces 100 parts in 40 minutes. So that's equal to what? 100 divided by 40, that's 2.5 parts per minute. And they told us A produces it twice as fast, so A is going to be twice that, so A is going to be 5 parts per minute. If each machine produces parts at a constant rate, how many parts does machine A produce in 6 minutes? So 5 parts per minute times 6 minutes. 6 minutes is equal to what? Minutes cancel out, 6 times 5 is 30 parts. Choice A. 88. A necklace is made by stringing n individual beads together in the repeating pattern red bead, green bead, white bead. Let's see. So, red, green, white, blue, and then yellow, and you keep repeating. If the necklace begins with a red bead, and ends with a white bead, then n could be equal to? So let's think about it, it starts with a red bead, and ends with a white bead. So let's think about this, if it's exactly a multiple of 5, if n is equal to exactly the number of beads in this pattern, then it'll always end with a yellow. So if n is equal to some multiple of 5, it could be 5, it could be 10, or whatever, then you're going to end with a yellow bead. That makes sense. If you have 10, you'd just have the pattern twice. If n is equal to some multiple of 5 plus 1, then you're always going to complete the cycle completely, and then your going to have one more, and you're going to end with a red bead. I think you see the pattern here. If n is equal to some multiple of 5, and then it has 2 left over, or when it's divided by 5, it has a remainder of 2, you're going to end with a green bead. The multiple of 5 parts, you're going to complete all the way to yellow, and you're going to have 1, 2 left. And so if n is equal to a multiple of 5 plus 3, then you're going to end with a white bead. So a multiple of 5 plus 3 is essentially any number that ends with either an 8 or 3, because a multiple of 5 ends with either a 5 or a 0. So let's see what choices they give us. They give us 16, not a multiple of 5 plus 3. 32, not a multiple of 5 plus 3, 41 is not, 54 is not. 68, that is a multiple of 5 plus 3. It's 65 plus 3. 65 is 13 times 5, that's equal to 13 times 5 plus 3, so the choice is E. Problem 89. In the x-y coordinate system, if a, b and a plus 3, b plus k are two points on the line defined by the equation x is equal to 3y minus 7, then k is equal to what? Well I think an easier thing to do is to-- well actually we could just stay-- let's just define y in terms of x. So you get x plus 7 is equal to 3y, y is equal to 1/3 x plus 7 over 3. OK, let's see what we can do. So the slope of this line is 1/3, if you remember from algebra, this mx plus b form, but this is how fast the line goes up or down, this 1/3. Every move to the right in x by 1, you're moving up in y by 1/3. So what's the slope? If you give me two points, what's the slope? What's the change in y over the change in x? So I'll call this y1 and this is y2. Or point 1 and point 2, so you could say change in y is b plus k, the latter y point minus the first y point, over a plus 3 minus a. And what does this reduce to? b plus k minus k, b's cancel out, a plus 3 minus a, a's cancel out, I'm left with k over 3, and that equals the slope. We already know the slope is equal to 1/3. k over 3 is equal to 1/3, so k is equal to 1. It's choice D. Problem 90. At the rate of m meters per second, how many meters does a cyclist travel in x minutes? So remember, this is tricky. They said x meters per second, how many meters does a cyclist travel in x minutes, so let's get x in terms of seconds. So x minutes is going to be 60x seconds, because you have 60 seconds per minute. So 60x seconds. And distance is equal to rate times time, hopefully that's a little bit of intuition for you now, but the rate is equal to m meters per second, and he's traveling for 60x seconds, so you get m times 60x, which is 60mx in seconds, times meters per second, that's meters. So 60mx meters. How many meters does a cyclist travel in x minutes? x minutes is 60x seconds. How many meters does a cyclist travel-- right, rate times time, at a rate of m meters per second. I think they made a boo-boo here, because they have to have the 60m-- oh, I see the mistake I made. Let me redo it, my bad. They said, at the rate of m meters per s seconds, so the cyclist's rate is actually m over s meters per second. That's confusing because they said that s seconds, and I thought they said, m meters per second, but it's a rate of m meters per s seconds, how many meters does a cyclist travel in x minutes, which we know is 60, if it's x minutes, it's 60x seconds. So you multiply the rate times the time, and you get 60mx over s, which is choice E. And it saved me that my original answer wasn't anywhere in any of the choices. Problem 91. If Sam were twice as old as he is, he would be 40 years older than Jim. So 2 times Sam, so if Sam were twice as old as he, so s is Sam's current age. If Sam were twice as old as he is, he would be 40 years older than Jim, so he would be Jim plus 40. If Jim is 10 years younger than Sam, how old is Sam? Jim is 10 years younger than Sam, so we can say Sam is Jim plus 10. We could've also said Sam minus 10 is equal to Jim, same thing. Let's see what we can do here, let's see how best we can solve this equation. They want to know how old is Sam. We want to solve for s, so let's do something. Let's subtract this equation from that equation. So 2s minus s is s, j minus j is 0, 40 minus 10 is 30. So Sam is 30, and we're done. And there's a lot of ways you could've done that. You could have solved for j, and substituted here then solved, it would've taken a little bit more time, but we just subtracted this equation from that, and you got s is equal to 30, which is choice B. And I think I'm about out of time, so I'll continue into the next video. See you soon.