Posted on 11/16/2009 5:57:35 PM PST by netmilsmom
Okay, we have tons of algebra programs that can work with numbers but do not have any help with Story problems.
Can anyone tell us the formula for solving this, step by step.
Nine pounds of Sweet Potatoes cost the same as Six pounds of Apples. One pound of Sweet Potatoes cost twice as much as one pound of Onions. While a pound of Apples costs 24 cents more than a pound of Onions.
(we can't solve it with NO integers)
Can anyone tell us how to do this?
Excellent!
How far down this thread do I have to go to find a serious attempt at an answer?
Bunch of wise guys around here.
The inchworm is on the rubber band. He does get transported with the rubber band when it stretches.
So at the end of the first minute, the inchworm has traveled 1 inch (at this time the rubberband is still 8 inches long). (the inchworm has traveled 1/8 the distance of the rubber band). At the end of one minute the rubber band instantaneously stretches 8 inches (at this step it has doubled its length). The inchworm is still at 1/8 of the length of the rubber band, but 1/8 the length of the rubber band is now 2 inches. At the end of the second minute, the inchworm moves another inch and is now at 3/16 the length of the ruber band. At this time the rubber band once again instantaneously stretches 8 inches to 24 inches in length. So the actual distance now is at 24 * 3/16 = 4.5 inches out of 24. And So on.
Its basically a Sum(1-x) of (1/8x) = 1...where you get
1/8 + 1/16 + 1/24 + 1/32 +.....=1.
The number is large enough to approximate an integral, so
INT(1-x) of 1/8X = 1/8* Ln(x) - ln(1) = 1
So since Ln(1)=0 then
1/8 * ln(x) = 1
ln(x)=8
x=e^8 = 2981 (minutes)
the length of the rubber band at this time is
8 + 2981 * 8 = 23856 inches = 1988 feet
Best is #118
This may be a little late but, welcome Newbie.
Haven’t read through the thread so don’t know if you’ve gotten your answer yet, so I will go ahead and post what I got and hope its right!
Let p=sweet potatoes
let a=apples
let o=onions
From the story:
9p=6a
1p=2o
a=o+.24
Now begin substituting:
9p = 6(o + .24)
9p = 6o + 1.44
Substitute again:
9p = 18o, therefor
18o = 6o + 1.44
12o = 1.44
o = .12
a = o + .24, so a = .36
p = 2o, so p = .24
Answers:
o=.12
a=.48
p=.24
‘Ave we already covered subject/verb agreement, Mate?
1988 feet? That’s a long rubber band.
I mean, a=.36
You should just show the answer and close with the old line, “The derivation is left to the student.” Teachers loved to use that one.
Well done! I LOVE Algebra! Was looking thru the thread to see if anyone had solved it before I gave it a shot! :-)
Watch it! ;-)
1/8 + 1/16 + 1/24 + 1/32 +.....=1.
Yes, and you need 1667 elements in this sum to get to 1. So the worm needs about 1660-1670 minutes, depending on precision of calculation. Mathcad says 1677 is enough.
The number is large enough to approximate an integral, so
But no, you can't do that. The scenario calls for a step function when you stretch the band. My formula for v(t) in the original calculation was this: v(t) := 1/(1+floor(t))
I also noticed that if I use v(t) := 1/(1+t) then indeed I get your answer, which is 2981. But that calculates for *continuous* stretching of the band, which is against the rules. It takes longer because it is advantageous to the worm to crawl as much as possible on the "shorter" band, before it is stretched. I even plotted both functions (distance/time) to be sure. When you substituted the sum of discrete components with a continuous integral you changed the rules of the game, and the result is very different.
Hmm, I think I stand corrected. This problem was originally given to me by a crazy old chemist who loved math problems. At the time, I thought doing it with an integral would be correct, but now in retrospect I see the error, as you are correct, the integral turns the rubber band stretching continuous rather than discreet (over all possible values of x as opposed to just integers). The old chemist was wrong as well, lol.
I saw the error, but it was too hard to go back and correct. Now I'm on a regular keyboard again and my standards are higher.
Since the mess boys already ate the strawberries we have no way of knowing the answer to that.
Glad she got to really understand the problem. I don’t know switched on schoolhouse; is it a video series? I’d really recommend you look at the appropriate Saxon book next year. Maybe see if a homeschooling friend has a copy you can read through yourself. The word problems in Saxon are a lot more intuitive.
Isn’t it funny how many different ways there are to solve math problems? And how many different ways people can explain the same thing? I think this thread is a great experiment in this. We should bookmark it for homeschooling freepers. After this they can just freepmail the person whose answer they found the most intuitive for help :D
I had a professor in college whose catchphrase was “And the answer just so happens to be...”
Speaking of racists. There was an article up on Fox Nation the other day about Bill Ayers saying that Hillary is a racist. That he knew that she was speaking in racist code while campaigning.
Looks like a preemptive strike against her heinous. Let them destroy each other with their madness.
Too bad they’re taking America down with them.
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