We’re on test 8 section 5, page 855. Problem one, if x/x-2=39/37 then what does x equal? And here you could try to solve this equation but this is a pattern here that you can actually identify immediately. If x=39 then what is x-2? X-2 is going to be 37. So you can immediately just try out these numbers and that’s going to distract because 37 is two less than 39, x-2 is two less than x so x must be 39. You could do that problem really fast.
If you do not know still what I’m saying you could kind of solve it in a traditional method cross multiply. We could say 37x=39(x-2) so you’ll get 37x=39x-78 and then you can subtract 39x from both sides, and then you’ll get -2x=78. Divide both sides by two and you’ll get x=39. Well that would taken a lot of variable time and the first problem in any essentially the SAT if you cannot do it in ten seconds you might be doing it the wrong way. It’s normally a very, very quick problem and that’s why this probably was not the correct way of doing it. You could’ve just said “Well, x is 39, x-2 is 37”.
Next problem, problem two, students in advanced Biology class. So okay, so they have boys, girls, total, and then on this side, it was juniors, seniors and then total, and then you write something just like k, n, m, r, s, t, w, x, z. And the table above, each side of them represents the number of students in that category. K would be the number of junior boys in the advanced Biology class. Which of the following must be equal to z? So z is the total number of kids, right? So there are a couple things that could be equal to z. It could be w+x with that sum of choice. It could also be m+t, but that is not a choice either, right, m+t isn’t the choice.
And what the other way is you could just add up all of the kids that are in each of the categories. So z is the total of all the kids so if you say the number of junior boys plus senior boys plus junior girls plus senior girls. So that’s k+n+r+s, that’s all the students in the class and that must equal z and that is choice E.
Next problem, so they have a line here, like that and then what did they tell us? They tell us that this right here is 25 degrees. This is A, B, C. This is 60 degrees and this is x and the triangle A, B, C above what is the value of x? This is just the angle game. So the first thing we want to figure out is this angle. We know that this angle plus 60 is going to be 180, right because it’s supplementary. They’ve kind of combined to form 180 degrees or they kind of create a line or go half around the circle. So this has to be 120, right because this plus 60 is 180.
And then we see that 25+120+x have to be 180 because they are all on the same triangle. So 25+120+x is going to be equal to 180 as well, so 145+x is equal to 180. Subtract 145 from both sides, you get x=35, right 80-45=35 and that’s choice C.
Next problem, problem four, now Martin’s refrigerator is broken and it will cost $300.00 to fix. A new energy efficient refrigerator costing $900.00, so let’s say this other refrigerator costs $900.00. It will save $15.00 a month on the electric bill. If they buy the new refrigerator in x months the Martin’s would have saved an amount equal to the difference between the cost of the new refrigerator and the cost of the old one. What is the value of x?
Okay, so they’re saying that if in x months the Martin’s are going to save an amount equal to the difference between the cost of the new refrigerator and the cost of fixing the old one. So what’s the cost of the new refrigerator? It’s $900.00 and what’s the cost of fixing the old one? It’s $300.00. So that’s the difference between the cost of fixing the new refrigerator and the cost of fixing the old one.
And the say that, that’s how much they would have to save in x months. They’re going to save that in x months. They say it’s $15.00 a month, right? So $15.00 times x months has to be equal to this. It’s the difference in price essentially of fixing or buying and this is a times or minus times. So you’ll get 600=15x, so x=600/15, so x=40. So that’s choice D, it takes 40 months for them to break unit.
Next problem, problem five, the perimeter of an equilateral triangle ABC is three times the perimeter of equilateral triangle D. So this is one of them and the other one actually is smaller. So if I call this one A, B,C, this one is D, E,F. You see the perimeter of this one is three times this one and they’re both equilateral, so this is x, x, x and so we do not know what these sides are but the perimeter of this one will be 3x. They tell us if the perimeter of DEF is ten, what is the length of one side of ABC?
So perimeter of triangle DEF is equal to ten and they tell us that the perimeter of ABC is three times this, right? So that means that the perimeter of triangle ABC is going to be three times this. So it’s 30, right? So the perimeter of this triangle is 30 and it has three equal sides so each side has to be ten, right 30 divided by 3 and that’s choice B.
Next problem, problem six, a machine mints coins at the rate of one coin per second. If it does this for ten hours each day, approximately how many days will it take the machine to mint 360,000 coins? So let’s say how much it produces in one day?
So let’s see. In one day it will be producing for ten hours per day times how many seconds per hour times 3600 seconds per hour and how did I get 3600? 60 minutes per hour times 60 seconds per minute. That goes with 3600 times one coin per second. The units actually cancel out. The hours cancel out with hours and then you get seconds cancel out with seconds and you have coins per day. So that equals ten times 3600 is 36,000 coins per day.
So the amount of coins that produce in d days is going to be 36,000 x d, times the number of days and that we’re saying has to be equal to 360,000. Well let me just divide both sides. Well, d will be 360,000/36,000 and so that cancels out with that, if 360/36 and that just equal to ten. So it would take ten days to produce 360,000 coins and that’s choice A.