# 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:** 3
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 8, 2009, 8:01pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/41 "2009-10-08T20:01:20Z")
First equation is correct; the second equation is multiplying the wrong thing by two. Also, remember that, for instance, 2x + 7 and 2 (x + 7) are not the same thing – you seem to make this mistake pretty consistently. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 8, 2009, 8:29pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/42 "2009-10-08T20:29:02Z")
W - 6 = N + 6 N - 6 = 2(W + 6) But something is wrong with my signs. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 8, 2009, 8:32pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/43 "2009-10-08T20:32:20Z")
Read the second “if” sentence again. Who would have twice what? ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 8, 2009, 8:37pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/44 "2009-10-08T20:37:15Z")
Wally would have twice as many shirts as Norm, so 2N = W + 6? ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 8, 2009, 8:39pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/45 "2009-10-08T20:39:07Z")
So Norm has 12 shirts and Wally has 18? (Damn, I feel like I’ve just given birth without an epidural.) ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 8, 2009, 8:52pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/46 "2009-10-08T20:52:49Z")
> [@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. I’ve skipped a step in the exposition. 1/30 = t + 1/30 has a solution: t = 0. That’s not physically feasible, however, so there’s no solution to the problem as posed. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 8, 2009, 8:53pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/47 "2009-10-08T20:53:35Z")
Dammit, that shirt answer is not right. ☹ ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 8, 2009, 9:06pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/48 "2009-10-08T21:06:51Z")
Nope, it’s not. Okay, try again. (W \*\*- \*\*6) = (N \*\*+ \*\*6) is correct. The other “if” sentence is based on (W **+** 6) and (N **-** 6). Which side of that needs to be multiplied by two? ---
**Author:** ![Mtgman](https://avatars.discourse-cdn.com/v4/letter/m/b5a626/32.png) [@Mtgman](https://boards.straightdope.com/u/Mtgman)\ **Post date:** [October 8, 2009, 9:20pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/49 "2009-10-08T21:20:39Z")
> [@Bricker](#): > > A house is twice as old as its oven was when the house was as old as the oven is. The sum of their ages is 49 years. How old is the oven and how old is the house? There’s basically two ages for each item, we’ll call them H[sub]1[/sub] and H[sub]2[/sub] and for the oven we’ll have O[sub]1[/sub] and O[sub]2[/sub]. In both cases the Item[sub]1[/sub] is the older(longer ago) age of the item in question and Item[sub]2[/sub] is the current age. Let’s list what we know. H[sub]2[/sub] + O[sub]2[/sub] = 49 H[sub]2[/sub] \* 2 = O[sub]1[/sub] H[sub]1[/sub] = O[sub]2[/sub] That looks right to me. Anyone else get any other relationships out of it? It wasn’t the clearest wording. Enjoy, Steven ---
**Author:** ![nivlac](https://avatars.discourse-cdn.com/v4/letter/n/3bc359/32.png) [@nivlac](https://boards.straightdope.com/u/nivlac)\ **Post date:** [October 8, 2009, 9:25pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/50 "2009-10-08T21:25:50Z")
> [@ivylass](#): > > … where did I go wrong? 30 + 90 = 120, divided by two miles = 60mph. This tells me that you still need to bone up on fundamentals. Without even doing the math, the units don’t even match up. You have mph divided by miles and you get mph out of that? No way. When you set up equations, always check that the units match up or you’ll end up with nonsense. ---
**Author:** ![Baker](https://avatars.discourse-cdn.com/v4/letter/b/bb73d2/32.png) [@Baker](https://boards.straightdope.com/u/Baker)\ **Post date:** [October 8, 2009, 9:42pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/51 "2009-10-08T21:42:02Z")
> [@ivylass](#): > > **Baker** , I had no idea how to even start figuring that one out. Can you explain how you go the answer? 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. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [October 9, 2009, 7:05am UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/52 "2009-10-09T07:05:57Z")
> [@ultrafilter](#): > > I’ve skipped a step in the exposition. 1/30 = t + 1/30 has a solution: t = 0. That’s not physically feasible, however, so there’s no solution to the problem as posed. Having no solution is what many people consider a “trick question.” You are often taught that, if you get a ridiculous answer, you must have done something wrong. Especially back in Algebra I, where you are just learning the basics and are more likely to make mistakes. ETA: Let’s see if I can come up with an example for the OP in less than 5 minutes. Meh, how about just a link: > **[Classzone.com has been retired | HMH](https://www.hmhco.com/classzone-retired)** ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 9, 2009, 3:10pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/53 "2009-10-09T15:10:22Z")
> [@ultrafilter](#): > > Mary is driving a two mile stretch of road, and she’s taken the first mile at 30 mph. At what speed will she have to drive the second mile so that her average speed is 60 mph? I think I see where my confusion is. Nowhere in this question does it state Mary has to average 60mph over the two miles. So, I stand by my earlier answer…if she wants to average 60mph, she has to drive 90 mph for the second mile. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [October 9, 2009, 3:32pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/54 "2009-10-09T15:32:19Z")
> [@ivylass](#): > > Nowhere in this question does it state Mary has to average 60mph over the two miles. That’s exactly what “At what speed will she have to drive the second mile so that her average speed is 60 mph?” This is a pretty standard algebra question, and your approach is the classic wrong answer. [Here](http://www.algebra.com/algebra/homework/Average/Average.faq.question.174775.html) is another version with the same wording and explanation. ---
**Author:** ![RadicalPi](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/radicalpi/32/9806_2.png) [@RadicalPi](https://boards.straightdope.com/u/RadicalPi)\ **Post date:** [October 10, 2009, 7:14am UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/55 "2009-10-10T07:14:41Z")
6 31 156 \_\_\_ 3906 Answer: 781 Explanation: The difference between any term and the next term is an increasing power of 5. That is, 6 + (5×5) = 31, and 31 + (5×5×5) = 156, and 156 + (5×5×5×5) = 781, and 781 + (5×5×5×5×5) = 3,906. The pattern starts somewhere in the middle. Starting with no fives at all gives 0, 1, 6, 31, 718, 3,906, 19,531, 97,656, and so on, which are just the sums of the powers of five. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 10, 2009, 1:25pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/56 "2009-10-10T13:25:48Z")
Your answer is right, and I think your explanation is also – but there’s an easier explanation. (Well, easier for me to understand, though I admit I’m not naturally a math person.) Multiply each number by 5 and add 1. (6 x 5) + 1 = 31 (31 x 5) = 1 = 156 etc. ---
**Author:** ![ivylass](https://avatars.discourse-cdn.com/v4/letter/i/9de053/32.png) [@ivylass](https://boards.straightdope.com/u/ivylass)\ **Post date:** [October 10, 2009, 2:15pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/57 "2009-10-10T14:15:58Z")
I knew there were multiples of 25 (or 5) involved, just subtracting the difference between the numbers, but that’s as far as I got. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [October 10, 2009, 2:21pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/58 "2009-10-10T14:21:03Z")
You’ve got a T-shirt problem to finish, missy! **stern look** ---
**Author:** ![Randy\_Seltzer](https://avatars.discourse-cdn.com/v4/letter/r/ee7513/32.png) [@Randy\_Seltzer](https://boards.straightdope.com/u/Randy_Seltzer)\ **Post date:** [October 10, 2009, 4:47pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/59 "2009-10-10T16:47:05Z")
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: You are paddling your kayak up a river. The river flows at 3 mph and your rowing speed is 4.5 mph – slightly faster than the current. You drop your hat into the water. 45 minutes later, you notice your hat is missing, execute a magical instantaneous turn, and paddle back down the river at the same constant speed. How long will it take you to catch up with your hat? And a more traditional algebra problem: You and your friend need to get to the airport from the hotel. You take the taxi which charges $2.25 for a flag drop and $0.75 per mile after that. But today is International Taxi Day, so the cabbie automatically takes 10% off the total fare. Your friend takes a rickshaw, which charges $3.25 for the flag drop, and $0.50 per mile after that. You meet at the airport and discover that you both paid the same amount for transportation. How far is the airport from the hotel, and how much did you each pay? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [October 10, 2009, 6:31pm UTC](https://boards.straightdope.com/t/give-me-some-math-problems/513062/60 "2009-10-10T18:31:22Z")
> [@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: > > You are paddling your kayak up a river. The river flows at 3 mph and your rowing speed is 4.5 mph – slightly faster than the current. You drop your hat into the water. 45 minutes later, you notice your hat is missing, execute a magical instantaneous turn, and paddle back down the river at the same constant speed. How long will it take you to catch up with your hat? > > And a more traditional algebra problem: > > You and your friend need to get to the airport from the hotel. You take the taxi which charges $2.25 for a flag drop and $0.75 per mile after that. But today is International Taxi Day, so the cabbie automatically takes 10% off the total fare. > > Your friend takes a rickshaw, which charges $3.25 for the flag drop, and $0.50 per mile after that. > > You meet at the airport and discover that you both paid the same amount for transportation. > > How far is the airport from the hotel, and how much did you each pay? The cabbie problem: Let _m_ = miles travelled. You have 9/10 (2.25 + 0.75_m_) = 3.25 + 0.5_m_ Multiply through by 10: 9 \* (2.25 + 0.75_m_) = 10 \* (3.25+ 0.5_m_) Multiply through by 4: 9 \* (9 + 3_m_) = 10 \* (13 + 2_m_) Multiply out: 81 + 27_m_ = 130 + 20_m_ Collect terms: 7_m_ = 49 _m_ = 7 Substitute in the original equation (the second equation is easier): Payment = $3.25 + $3.50 = $6.75 The canoe problem:Consider the river as a stationary frame of reference, when the position of the hat does not vary. It therefore takes as long to paddle back as it did to get upriver: 45 minutes. Of course the hat is a lot further downstream than it was when you dropped it, but you weren’t asked about that. [Previous page](https://boards.straightdope.com/t/give-me-some-math-problems/513062.md?page=2) [Next page](https://boards.straightdope.com/t/give-me-some-math-problems/513062.md?page=4)