At what age range are these things taught in America? I learned them around 12-13.
I don’t have an problems to offer off the top of my head, but I can suggest a couple of study resources.
There’s a series of books called “Schaum’s Outlines”. They are mostly on math and science topics but there are other topics as well. I used them in college and in grad school. I found them to be very clear and straightforward. The outlines have a lot of worked problems as examples, and those examples are very illustrative. Schaum’s outlines are also very affordable, or were when I was in school.
Wikipedia link: Schaum's Outlines - Wikipedia
Current publisher’s web site: http://www.mhprofessional.com/category/?cat=3700
Even today’s editions look to be under $20 a copy. Your local library may have them as well. My only connection with them is as a customer.
A web site with homework help, and other resources, mostly for algebra http://www.purplemath.com/
The writer contributed to a Usenet group I used to participated in called alt.algebra.help - I remember her writings as being particularly clear.
A simple problem I got from a chapter of trick questions from Scientific American, which does have an algebraic solution.
A fish weighs 20lb plus half its own weight. What is the weight of the fish?
That’s the problem. Unless one uses them every day, one tends to forget how they work (factoring, multiplying fractions, word problems…it truly is, use it or lose it.)
I’m working on the t-shirt problem…promise!
I had Algebra I in 8th grade, Geometry in 9th, then Algebra II, then Trig.
House is 28 years old, oven is 21 years old.
The fish weighs 40 lb.
Sources of good practice problems:
REA Problem Solvers
SAT Practice Tests
GRE Practice Tests
Thanks…that second formula was eluding me.
Okay, here’s an easy one:
Alison is now one-third as old as Samantha. In six years, Alison will be as old as Samantha is now. How old are they now?
Sam is 9, Alison is three.
Told you it was an easy one! 
Restored my confidence, there!
You’re driving down a stretch of highway that normally takes you 25 minutes to drive at 60 miles per hour. Some traffic congestion made the first 10 miles take 15 minutes to navigate. How fast do you have to drive the remaining stretch so that the whole drive still takes 25 minutes?
Note: professional driver on closed course. Do not attempt.
Here’s a little cheat for you:
“Is” -> =
“per” -> divide
“of” -> *
“and” -> +
“minus”, “without”, etc -> -
So the sentence is
The fact that is says “tracy is three times…” means that you should automatically know the formula will start “T = 3*…” because of the word ‘is’. Remember that.
This is also useful when someone says “5 dollars per donut” Then you know it’s “5/1 dollars/donut” because I used ‘per’. Also, “half of the people” translates to “.5*p” because of the word ‘of’.
So you can do the fish example easily with this. “A fish is twenty pounds plus half of it’s weight.” Without even comprehending the sentence, you can write out “F = 20 + .5F” and solve from there.
Neato, amiright?
You used the diameter as the radius.
You didn’t ask to solve for t. You asked to solve for R2, which is infinity. Why are you expecting someone to plug in numbers before situating the variables? If you do it without any number substitution, you keep getting divide-by-zero. That’s certainly a trick question in my book.
h = 1.5
d = 9 = 2r
r = 4.5
H = 2
R = radius of second cake set
D = diameter of second cake set
m= 2cakes * pi * r^2 * h
m= 2pi * 4.5^2 * 1.5
m = 3pi* 4.5^2
3m = pi * R^2 * H
3m = 2pi * R^2
**3(3pi *** 4.5^2) = 2pi * R^2
9pi * 4.5^2 = 2pi * R^2
4.5 * 4.5^2 = R^2
R =4.5 ^ 1.5
D = R*2 = 4.5^1.5 *2 = 19.091 inches.
The bolded part is where you messed up. I think you made it 6pi the first time around instead of 9pi. So technically, you found it for 2 mixes. But that’s not the math error, you did, I don’t think. Of course, I’m attempting to be psychic here.
You erred when you thought that averaging the numbers will average your speed. This doesn’t make sense if you put it in the extreme. I travel 1 mile at the speed of light. I then travel the next mile at a speed of 0 mph. How long does it take me? Not c/2, as you gave. If I stop halfway there, my average approaches 0 the longer I sit there, right? Here’s the key, so pay attention: The problem is giving a variable speed over an equal distance. You can only arithmetically average the speeds if it’s over an equal time.
In D/T = R, if the T is the same over both segments, you can just average the R. If D is the same, you can’t.
The average of 10/1 and 30/1 is 20/1, right? Because (10+30)/2= 20.
The average of 1/10 and 1/30 is not 1/20. It’s 1/15.
If you don’t want to do the math for these types of problems, you can memorize that the denominator (here, the 15) is 2ab/(a+b). Just cuz it is. If you care, here’s why:
So, here’s a quick example. Remember this is over equal distance. I travel for 32 miles at 45 mph. I then travel the next 32 miles at 16 mph. What’s my average? Note: I gave you non-easy numbers for a reason.
24516/(45+16) = 23.6 mph.
Hope that helps.
Okay, let’s the stretch of road is 60 miles long. It takes her 25 minutes to go 60 miles. She has 50 miles still to travel in 10 minutes? I believe she will be delayed further when a police officer pulls her over for speeding!
I’m coming up with 300mph, but I wouldn’t be surprised if that’s wrong.
I hate this. It’s like having the word on the tip of your tongue, but you can’t get it out.
Chessie, those cheats are very helpful. Thank you!
Hint; no, it’s not 60 miles long. The average speed you maintain along the road (under normal conditions) is 60mph. At that average speed, it takes 25 minutes to drive.
How long is the road?
25 miles; 25 minutes at an average of a mile a minute.
Correct.
Which means that when the house was as old as the oven is now, the house was 21 years old. That was 7 years ago, so the oven was 14 years old.
Which makes the house, NOW, twice as old as the oven was back then.
Dammit. :smack:
Okay, that leaves her having to drive 15 miles in 10 minutes. 90 mph?
So, two things. First, I gave you a rate of speed problem, which is probably the trickiest kinds of algebra problems you’ll see on the test. Then, to confuse things further I gave you numbers with different units. I gave you miles per hour but then gave you time in minutes. To get the answer you either have to convert the two numbers to use the same units.
The easiest way is to convert the speed to miles per minute. 60 miles per hour and 60 minutes per hour, so 1 mile per minute.
On edit: yep, 90 mph is right.