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CAHSEE practice: Problems 20-22

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Problem number 20. At a local bookstore, books that normally cost b dollars are on sale for $10 off the normal price. So not just $10, it's $10 off the normal price. So if the normal price is b. So b is the normal price. The sale price is $10 off the normal price, or b minus 10 is the sale price. How many dollars does it cost to buy 3 books on sale? So each book on sale is going to be b minus $10. So if you buy 3 of them, you just multiply that times 3. So it's going to be 3 times b minus 10. And you see that choice right there. Now if they didn't write like this, if they multiplied it out, you would just distribute the 3. So it would be 3 times b, which is 3b, minus 3 times 10 or 30. But that's not one of the choices right there. And then lucky for us, this choice is there. 3 times b minus 10. b minus 10 is the cost of each book on sale, $10 off the normal price. Problem 21. If a line passes through the points A and B shown below-- so this is A and this is B-- approximately where does the line cross the x-axis? Approximately. So they just want us to get a sense. So they're talking about this line. Let me draw it here. This line right there, and I just keep going like that. Do my best to draw it straight. If you had another pencil, you could actually draw it perfectly. And so where does it cross the x-axis? The way I drew it, it does cross the x-axis right there. So let's see which of these say that. So between minus 3 and minus 2. Well, yeah, I mean just the way I drew it, this wasn't exact, but that looks pretty good. So I'll underline this. If there were some other choices that were close to that, I'd have to be a little bit more exact. But let's see what the other choices say. Between 0 and minus 1. Well, that means here. And clearly the line didn't cross anywhere near there, so that's definitely not our answer. Between 0 and 1. The line was nowhere near there, so it's not there. Between 1 and 2. Clearly not there. So we can be very confident that our choice is A. Out of all of the choices, that's the one that even gets close to where even my rough drawing crossed the x-axis. Actually, even my rough drawing did go right between minus 3 and minus 2. Problem 22. Which expression is equivalent to this thing right here? Let me rewrite it. So we have 7 times a squared times b, times 7 times b times c squared. So when you have multiplication, it's actually commutative. You can switch the order of multiplication. So if we just switch the order of this, we could say that this is the same thing as 7 times 7 times a squared, right? 7 times 7. That's that right there. And then you have times an a squared. That's that right there. And then you're left with these two b's, so you could say times b times bc squared, right? That is that right there. And so we can just rewrite this. 7 times 7 is 49. a squared is just a squared. b times b is b squared, and then you have a c squared. So it's 49a squared, b squared, c squared. Which is choice C. 49a squared, b squared, c squared.