My Math Forum System of Equation: Value Problem

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 August 3rd, 2018, 03:51 AM #11 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,282 Thanks: 931 Ebba, good place to practice similar problems: https://www.purplemath.com/modules/coinprob.htm Thanks from greg1313, topsquark and Ebba Sen Pai
 August 3rd, 2018, 08:57 AM #12 Senior Member   Joined: May 2008 Posts: 293 Thanks: 79 Beer soaked recall follows. I just went through volume 12 of The Complete Peanuts a few weeks ago and this coin problem by Ebba Sen Pai reminded me of a problem faced by Peppermint Patty way back in 2.26.1974 where she read: A man has 20 coins consisting of dimes and quarters. If the dimes were quarters and the quarters were dimes, he would have ninety cents more than he has now. How many dimes and quarters does he have? Unusually sober at the time, I simply wrote it down for future reference. It seemed like the problem was out of place for a 4th grade (or was it 5th grade?) student. I know it's a problem routinely solved by Sir D with his eyes closed but it somehow gave me pause. Totally rusty. Had to go through a brute force approach for about half an hour (maybe more) before I finally visualized its solution as [.10*x+.25*(20-x)]-[.25*x+.10*(20-x)=-.95 Thanks from Denis and topsquark
 August 3rd, 2018, 09:55 AM #13 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,282 Thanks: 931 Sir J, I'm SURE that you would have solved instantly if that puzzle has been worded along the lines of: A man has 20 bottles of beer consisting of quarts and pints. If the pints were quarts and the quarts were pints, how many ounces....... Can't understand your solution; mine is (a bit long!): d + q = 20 ; q = 20 - d [1] .10q + .25d - .10d - .25q = .90 .15d - .15q = .90 ; divide by .15: d - q = 6 ; subs. [1]: d - 20 + d = 6 2d = 26 d = 13 q = 20 - 13 = 7 Edit: Skip would probably reduce above to ~2.1745...steps using sneaky stuff like: difference in number of coins = .90 / (.25 - .10) = 6 Thanks from jonah Last edited by Denis; August 3rd, 2018 at 10:19 AM.
August 3rd, 2018, 10:04 AM   #14
Math Team

Joined: Oct 2011

Posts: 13,282
Thanks: 931

Quote:
 Originally Posted by jonah [.10*x+.25*(20-x)]-[.25*x+.10*(20-x)=-.95
Ahhh...yer missing a half bracket, plus -.95 should be -.90:

[.10*x+.25*(20-x)]-[.25*x+.10*(20-x)]=-.90

x = 13 = dimes (which you did not "declare"!)

To the corner for .95 of an hour...with max. of 6 beers...

 August 3rd, 2018, 10:26 AM #15 Senior Member   Joined: May 2008 Posts: 293 Thanks: 79 Beer soaked surprise follows. Man, I totally did not notice those typos. Good catch Sir D. The corner is not good enough for my carelessness; I should be sent to the principal this time around for coming to class hammered. Thanks from greg1313 and Denis Last edited by jonah; August 3rd, 2018 at 10:30 AM.

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