# Give me some math problems **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [October 8, 2009, 4:41pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062 "2009-10-08T16:41:49Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [October 10, 2009, 8:17pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/61 "2009-10-10T20:17:49Z")
At what age range are these things taught in America? I learned them around 12-13. ---
**Author:** ![Typo\_Knig](https://avatars.discourse-cdn.com/v4/letter/t/cdc98d/32.png) [@Typo\_Knig](https://boards.straightdope.com/u/Typo_Knig)\ **Post date:** [October 11, 2009, 12:07am UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/62 "2009-10-11T00:07:48Z")
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](http://en.wikipedia.org/wiki/Schaum%27s_Outlines) Current publisher’s web site: [http://www.mhprofessional.com/category/?cat=3700](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/](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. ---
**Author:** ![MHaye](https://avatars.discourse-cdn.com/v4/letter/m/bbe5ce/32.png) [@MHaye](https://boards.straightdope.com/u/MHaye)\ **Post date:** [October 11, 2009, 12:28am UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/63 "2009-10-11T00:28:46Z")
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? ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 12, 2009, 12:52am UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/64 "2009-10-12T00:52:21Z")
> [@Quartz](#): > > At what age range are these things taught in America? I learned them around 12-13. 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! ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 12, 2009, 12:20pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/65 "2009-10-12T12:20:44Z")
I had Algebra I in 8th grade, Geometry in 9th, then Algebra II, then Trig. ---
**Author:** ![ianzin](https://avatars.discourse-cdn.com/v4/letter/i/ed655f/32.png) [@ianzin](https://boards.straightdope.com/u/ianzin)\ **Post date:** [October 12, 2009, 1:09pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/66 "2009-10-12T13:09:33Z")
House is 28 years old, oven is 21 years old. The fish weighs 40 lb. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [October 12, 2009, 5:38pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/67 "2009-10-12T17:38:55Z")
Sources of good practice problems: REA Problem Solvers SAT Practice Tests GRE Practice Tests ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 12, 2009, 6:59pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/68 "2009-10-12T18:59:14Z")
> [@Randy\_Seltzer](#): > > The T-Shirt Problem’s equations and solution (no work shown – you can still try to solve the equations yourself): > > W - 6 = N + 6 {If W gives N six, their new totals are equal} > W + 6 = 2 (N - 6) {If N gives W six, then W’s new total is equal to two of N’s new total} > . . . > N = 30 > W = 42 > And here’s a fun one that can be solved either slowly with arithmetic or quickly with logic: Thanks…that second formula was eluding me. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 14, 2009, 6:03pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/69 "2009-10-14T18:03:27Z")
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? ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 14, 2009, 7:29pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/70 "2009-10-14T19:29:51Z")
Sam is 9, Alison is three. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 14, 2009, 7:39pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/71 "2009-10-14T19:39:00Z")
Told you it was an easy one! 😉 ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 14, 2009, 7:48pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/72 "2009-10-14T19:48:41Z")
Restored my confidence, there! ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [October 14, 2009, 9:25pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/73 "2009-10-14T21:25:54Z")
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. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [October 14, 2009, 9:34pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/74 "2009-10-14T21:34:49Z")
> [@ivylass](#): > > I think I’m off with the 3T = B-2 part. Here’s a little cheat for you: “Is” -\> = “per” -\> divide “of” -\> \* “and” -\> + “minus”, “without”, etc -\> - So the sentence is > [@](#): > > 1. Tracy is now three times as old as Bob was two years ago. In four years, Bob will be as old as Tracy is now 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? > [@Mtgman](#): > > The key to **Baker’s** problem is the volume of a cake the mix makes. > > Checking **Baker’s** spoiler, I see our answers don’t match. I’ve double checked mine and I think it’s clean. If **Baker** posts his solution we can see where one of us went wrong. You used the diameter as the radius. > [@ultrafilter](#): > > Use d = rt. For the first leg, you get 1 = 30t, which gives t = 1/30 hour, or two minutes. Then use d = rt again to get 2 = 60(t + 1/30), which gives 1/30 = t + 1/30, and there’s no solution. 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. > [@Baker](#): > > Okay! The original problem read: > > \*You want to fill a large, single, round cake pan. One cake mix makes two layers 9" in diameter, and 1-1/2" tall. > > How big will the diameter be of a 2"tall pan that holds three cake mixes?\* > > First you need to figure the volume of the one mix, in the two smaller pans. You know they are round, and so you use the geometric formula for a cylinder, in this case a very short, squat cylinder. The formula is (r²)_(Õ)_(height)_(2), or (4.5_4.5)(3.14159)(1-1.5)(2). or 190.8515925 cubic inches. r=radius, which is one half the diameter of a circle. > > The resulting figure is multiplied by three, since you are looking for a pan that will hold three mixes. 190.8515925(3)=572.55477725 > > Now, you want a single 2" tall round pan with whose volume is that many cubic inches. > > So you go back to the formula for a cylinder. (r²)(Õ)(2")=572.55477725, or (r²)(3.14159)(2")=572.55477725. r² will be 91.125, the square root of which is about 9.54, and since radius times two is the diameter, the pan will have to be 19.08 inches across > > And I just realized now that my original spoiled answer was in error!:smack: > > Sorry for the confusion. The bad answer I gave was solving for two mixes, not for three. 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. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [October 14, 2009, 9:51pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/75 "2009-10-14T21:51:43Z")
> [@ivylass](#): > > **ultra** where did I go wrong? 30 + 90 = 120, divided by two miles = 60mph. 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: > [@](#): > > (1/a + 1/b) /2 = (a/ab + b/ab) /2 = (a+b)/2ab. Invert if you want the denominator, which you probably do. 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. 2_45_16/(45+16) = 23.6 mph. Hope that helps. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 15, 2009, 4:42pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/76 "2009-10-15T16:42:24Z")
> [@Punoqllads](#): > > 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. 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! ---
**Author:** ![MHaye](https://avatars.discourse-cdn.com/v4/letter/m/bbe5ce/32.png) [@MHaye](https://boards.straightdope.com/u/MHaye)\ **Post date:** [October 15, 2009, 4:58pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/77 "2009-10-15T16:58:06Z")
> [@ivylass](#): > > Okay, let’s the stretch of road is 60 miles long. 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. ---
**Author:** ![Bricker](https://avatars.discourse-cdn.com/v4/letter/b/977dab/32.png) [@Bricker](https://boards.straightdope.com/u/Bricker)\ **Post date:** [October 15, 2009, 4:58pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/78 "2009-10-15T16:58:50Z")
> [@ianzin](#): > > House is 28 years old, oven is 21 years old. 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. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 15, 2009, 5:27pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/79 "2009-10-15T17:27:43Z")
> [@MHaye](#): > > 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. Dammit. :smack: Okay, that leaves her having to drive 15 miles in 10 minutes. 90 mph? ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [October 15, 2009, 5:40pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/80 "2009-10-15T17:40:10Z")
> [@ivylass](#): > > 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. 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. [Previous page](https://boards.straightdope.com/t/give-me-some-math-problems/513062.md?page=3) [Next page](https://boards.straightdope.com/t/give-me-some-math-problems/513062.md?page=5)