You, Me, and Sally Goodtime meet at a bar for drinks.  Your drink costs ten dollars, my drink cost ten dollars, and so does Sally's.  When the waitress brings the bill she tells us she miscalculated the a check and tells us she owes the group five back.  Since she's so nice Sally convinces us that we should split the five with her.  So we each keep one dollar and give the waitress two.  That means we each paid nine dollars.  \n3 x 9 = 27\nAnd the waitress has two dollars.\n27 + 2 =29\n\nWhat happened to the extra dollar?
211063
The waitress calculation is wrong...\n\nYou me and Sally gave the waitress $10 each for a total of $30.\n\nThe waitress gave back $5\n\nWe gave the waitress back $2.\n\nTherefore, the waitress has $30 - $5 + $2 = $27
50003
It should be $27-$2, instead of $27+$2, since the $2 is included in the $27.
164832
I'd like to tell you a couple of tricks for getting ABOUT the right answer, which is often all you need, for instance when you're buying something and want to guard against a major cashier's error.\nMultiplying two numbers: Try to simplify the problem. Say it's 15 cans of something at 39 cents a can. Well 39 is pretty close to 40, so you get 15*40=$6.00. Or if you want it exactly, 15*40=$6.00 but subtract 15 cents because you added it when you simplified. $6.00 - $0.15 = $5.85. That's a lot easier than mentally multiplying 15 by 39.\nOften there seems to be no way to simplify the problem. Like 34 * $0.57. Well see what happens if you decrease one a little and increase the other by the same percentage. Say we take 34 down to 30, that's a little more than 10% less. Then what's a little more than 10% of 57? About 7. So we add 7 to 57, and we have 30 * $.64 = $19.20. The actual answer is $19.38. Again, not too bad. Or a 3-digit number: Try $3.79 * 18. OK, lets put $3.79 up to $4.00, about a 5% increase. Then take about 5% off 18 and it's 17. $4.00 * 17 = $68.00, compared to the exact answer of $68.22. \nHow about when you have a bunch of different items in the supermarket cart and you want the approximate total? Just keep track of the dollars and remember the cents as simple fractions of a dollar. So if you have these items: $1.39, $3.75, $2.19, $7.63, you say 1 & 1/3 plus 3 & 3/4 is 5 & a little; plus 2 & a little is 7 & 1/2; plus 7 & 1/2 is 15. The actual total is $14.96. Again, not too bad, although it won't always be this close. I hope you can use these. It gets easier with practice.
646660
You are adding the bellboy when he should be subtracted.  $27 -$2 = $25, which is what the room cost.  Since the room cost only $25, each man should get ~$1.66 back, but the bellboy robs them of $.33 each.  The total should be the cost of the room, which is $25, not $30.\n\nYes it is a riddle.  The trick is in telling the person that it adds to $29.  Without that, most people would probably just figure out that they had to subtract the $2, not add.
192328
the check was for $15.35\n\nthe method isn't beautiful, but whatever.  i got it.\nwhere x is the # of dollars the check was for, and y is the # of cents the check was for:\n2(x + y/100) = y + x/100 - 4.45\n2x + 2y/100 = y + x/100 - 4.45\n200x + 2y = 100y + x - 445\n199x - 98y = -445\n199x - 98y + 445 = 0 (mod 100)\n99x - 98y + 45 = 0 (mod 100)\n-x - 2y = -45 (mod 100)\n2y - x = 55 (mod 100)\n\nyou want y to be roughly (2x + 4) too.\n\nhey, how about y =35  --> x=15\n\n15.35*2 = 30.70\n35.15 - 4.45 = 30.70\n\nvoila!
208325
the other dollar is in your pocket.... you spent $97 dollars and had 3 dollars change... you payed back $2. of the $100.  you spent $97..... no matter how you look at it you had $3. and if you payed back 2 of the $3. the other Dollar is in your pocket.  the equation is 100. - 97 = 3 then 3 - 2 = 1 the dollar is in your pocket
233002
Easy. When the manager took $5 out of the $30 there was $25 remaining, right. That's $8.333333 paid each. When the bellboy gave them the $3 back that made it $9.333333 each. The remaining change from the $10 which is 67cents times 3 equals the $2 in the bellboys pocket.
655492
actually after taking 5 dollars from al of them they are left with \n8.3 each and when you give back a dollar to each its 9.3 each \n\nwhen you multiply by 3  its  28  plus  the 2 stolen dollars becomes 30.\nso there is no missing dollar.
161846
ok. there are 3 guys who go on a road trip. they go into the hotel and its $30.00 even for the room. so each guy pays 10.00. (10 x 3 =30)\nwhile they are in the room the checkin girl realizes its only $25.00 for the room. so she grabs 5 one dollar bills and goes up to the room. she realizes that 5 does not divide by 3 evenly. so she taked $2.00 and puts them in her pocket. as she knocks at the door she feels guilty and pulls the $2.00 out of her pocket. they ended up giving her 2 dollars and kept 3. if each guy gets 1 dollar back then instead of 10 they paid 9 each for the room. ( $9 x 3 = 27)\n27 + 2 (tip they gave lady) = $29.00\n\nWHERES THE LAST DOLLAR??????????????
664
The $2 should be subtracted from the $27, not added to it -- since they were overcharged by $5, the room actually cost $25.\n\nThey ending up paying $27, $25 for the room and $2 to the bellhop. That $27 plus the $3 refund is the original $30
394271
This is solvable, and you wrote it very well!\n\nThe key to setting this up is knowing that for any 2-digit number, you can write it as 10a + b.\n\nSo your problem states that a+b=9 (the sum of the tens digit and ones digit is 9), and it states that a=3b+1 (the tens digit is 1 more than 3 times the ones digit).\n\nSo now you have 2 equations in 2 unknowns, which you can easily solve for:\n\na + b = 9\na = 3b + 1\n\nSubstitute a = 3b + 1 into the first equation to get:\n\na + b = 9\n(3b + 1) + b = 9\n4b + 1 = 9\n4b = 8\nb = 2\n\nNow you can easily solve for a, which equals 7 since a+b=9.\n\nSo your 2-digit number is 72.\n\nCheck: 7+2=9\n7 = 1 + 3*2\n\nIt checks out, so our answer is correct!\n\n~ ♥ ~
439972
a) 4 is in the tens place, so it is worth 4 * 10 = 40\nb) 6 is in the ones place, so it is worth 6 * 1 = 6\nc) 3 is in the thousands place, so it is worth 3 * 1000 = 3000\nd) first 2 is in the hundreds place, so it is worth 2 * 100 = 200\ne) 7 is in the hundreds place, so it is worth 7 * 100 = 700\n\nOr you can just say the numbers and see what you say when you are on the underlined number...\n\n42 = "forty two" so 4 is "forty"\n176 = "one hundred seventy six" so 6 is "six"\n3049 = "three thousand forty nine" so 3 is "three thousand"\n1223 = "one thousand two hundred twenty three" so first 2 is "two hundred"\n10731 = "ten thousand seven hundred thirty one" so 7 is "seven hundred"
396452
Paula has twice as much money as Don. Together they have $105. How much does Paula have?\n\nP = 2D\nP/2 = D\n\nP + D = 105\nP + P/2 = 105\n\nSeventy two divided by a number is six. Find the number.\n\n72/X = 6\n\nJill's mother was 27 when Jill was born. The sum of their ages is now 51. How old is Jill?\n\nJill's mom is now 27 + J\n\nThe sum is 27 + J + J = 51\n\n\nThe product of a number and 18 is 270. Find the number.\n\n18X = 270\n\nThe sum of x and its square is equal to y times z.\n\nx + x^2 = yz\n\n\nTwice a increased by the cube of a equals b.\n\n2a + a^3 = b
387735
It looks like you have a typo in part of your check, where you put 8 instead of 7. But I see what you meant there.\n\nYour only problem is that you didn't apply the distributive property correctly.\n\nWhen you multiply 5 and (k^2 - 49), you have to multiply the 5 by everything in the parentheses:\n\n5 (k^2 - 49) = (5*k^2) - (5*49) = 5k^2 - 245\n\nNotice that we get back what you started with.\n\nYour factoring was correct, but you have that one small problem in your check.\n\nKeep at it!
232398
There isnt any money missing.  The men paid 30 dollars originally-$10 per person.  When the bellhop returned a dollar to each of them, that means that they paid a total of 27 dollars.  So, the motel got 25 of the dollars, and the bellhop kept 2 dollars.  Thats 27 dollars-nothing is missing.  The problem is that in the question you are adding the 2 dollars the bellhop kept to the 27 dollars the men paid, and that is logically wrong- You add the 2 dollars the bellhop kept to the 25 dollars paid to the motel.\n\nEach man did not pay 8.33-that makes no sense at all.  They each paid 10 dollars and got one back..simple math, they each paid 9 dollars.  Look at it a different way- forget that they paid 30 dollars to begin with, because that doesnt matter.  What they ended up paying is 27 dollars- 25 to the hotel, and 2 to the bellhop.\n*edit* Believe me, this question has been around a loooong time-they didn't each pay $8.33- use your logical mind for a second.  They each paid 10 dollars apiece, and then each got $1 back...how could you possible get to the point that they paid $8.33 from that?? And at any rate, by that illogic, there is still a penny missing.. how could you get a penny missing when the only thing that changed hands were dollars.  They each paid 9 dollars-thats a total paid out of 27 dollars.  25 to the hotel, 2 to the bellhop.  It's easy...don't get trapping the the illogical step of adding the bellhop's $2 to the patrons $27.  The patrons *don't have* 27 dollars, they have exactly $3!!. So, $25 to the hotel, $3 to the guests, and $2 to the bellhop-$30.
163201
nothing...the person who wrote that just took the wrong approach to finding the answer.  the math was just done wrong...\n\n10x3=30 each guy pays 10\n30-3=27 each guy get back one dollar\n27-2=25 the bellman pockets two\nthere are $25 left\n\nin the problem when the counter man keeps two they add it rather than subtract it like they should have
166913
there was total $30 in which you gave $3 and kept $2 to your self.so,the remaining $25 has to be split beetween the three so each dude gets $8.33.\nso the total would be\n9.33*3+2=30 dollars