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# CAHSEE practice: Problems 20-22

Video transcript

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.