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.
W - 6 = N + 6
N - 6 = 2(W + 6)
But something is wrong with my signs.
Read the second “if” sentence again. Who would have twice what?
Wally would have twice as many shirts as Norm, so 2N = W + 6?
So Norm has 12 shirts and Wally has 18? (Damn, I feel like I’ve just given birth without an epidural.)
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.
Dammit, that shirt answer is not right. 
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?
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
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.
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 (4.54.5)(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.
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:
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.
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 is another version with the same wording and explanation.
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.
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.
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.
You’ve got a T-shirt problem to finish, missy! stern look
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 + 0.75m) = 3.25 + 0.5m
Multiply through by 10:
9 * (2.25 + 0.75m) = 10 * (3.25+ 0.5m)
Multiply through by 4:
9 * (9 + 3m) = 10 * (13 + 2m)
Multiply out:
81 + 27m = 130 + 20m
Collect terms:
7m = 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.