Obsessing

So, I woke up this morning and guess what? I knew how to solve at least two of those stupid test problems! I didn't study last night; I didn't copy the questions in question and try to figure them out. I stayed home pouting about how badly I'd done, and watching a fairly dumb movie. But this morning I woke up knowing the problems (and I mean exact numbers) I was given to solve, and knowing just what to do anyway.

Stinky Problem #1:
Some stadium or other sells 33,000 seats; some of them are general seating for $4 each, and some are reserved seating for $13 each. They bring in $222,000. How many general seats and how many reserved seats did they sell?

Could I solve this yesterday afternoon? NO!!! I just sat there freaking out because I knew I should know how to do it, and trying everything I could imagine, and then finally left it unfinished.

I wake up this morning and, Bing! Here's how to do it:

G = general seating; R = reserved seating —OK?
So, G + R = 33,000 (general seats plus reserved seats equal the total amt. of seats sold).
4G = 13R = 222,000 ($4 per general seats plus $13 per reserved seat equals the total amt. of money brought in.)
To use the process of elimination I will get rid of the G from each equation. So I multiply the first problem by - 4, getting - 4(G + R = 33,000), or - 4G - 13R = -132,000. Follow?
Now I add that new problem I just created to the second problem and I get:
- 4G - 4R = - 132,000
+ 4G + 13R = 222,000 and the answer is:
9R = 90,000 or
R = 10,000

Since I now know that R = 10,000 I can figure out that G = 23,000 pretty easily. So the answer is:
They sold 23,000 general seating tickets and 10,000 reserved seating tickets. (And, yes, it checks out.)

See!!! I can do this! And it was easy besides!! And I could shoot myself for not being able to do it on the test yesterday! AAARRRRGH!!!

Stinky Problem #2: You row downstream with a 4 mph current at your back and you travel 94 miles. You come back only 47 miles in the same amount of time. At what rate do you row in still water? (Although I think saying "still water" is making an assumption.)
This morning I realized that I was three-quarters there with this problem, and if I hadn't been so freaked out I could have solved it.

Stinky Problem #3: A deep sea diving bell, traveling at a constant rate of speed goes down 600 feet in 8 minutes (which sounds like 75 feet per minute, but apparently isn't). It goes 1500 feet in 40 minutes (this sounds like 37.5 feet per minute). How fast was it really going?

Stinky Problem #4: A gas station sells 4289 gallons of gas at $1.35 per gallon; they sell 3570 gallons at $1.40 per gallon. How much could they sell at $1.19 per gallon? (A lot, nowadays!)

I'm still stuck on problems 3 and 4, although I'm sure I got close to solving them too, end even now the solution is tickling the edge of my brain.

I won't trouble you by solving problem 2 here on my blog. But getting 1 and 2 done would have been the difference between B- and A- on this exam. I really could shoot myself!

Can you do them?