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 April 12th, 2014, 11:01 PM #1 Newbie   Joined: Apr 2014 From: Texas Posts: 2 Thanks: 0 Word Problem Ok, this isn't homework. One of my coworkers asked the question. I was able to come up with the answer by trial and error, but could not figure out how to show it in mathematical terms. Chickens are 2 for a dollar. Pigs are 3 dollars each. Cows are 10 dollars each. You have to buy exactly 100 animals and spend exactly 100 dollars. How many of each animal do you buy? Answer: 5 Cows, 1 Pig, and 94 Chickens How do I express that in mathematical terms? Last edited by Darkwing; April 12th, 2014 at 11:08 PM. April 13th, 2014, 12:36 AM #2 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 c --> Chickens p --> Pigs w --> cows c/2 + p/3 + w/10 = 100 c+p+w = 100 Last edited by sivela; April 13th, 2014 at 12:44 AM. April 13th, 2014, 01:36 AM #3 Senior Member   Joined: Apr 2014 From: UK Posts: 955 Thanks: 342 Erm, not quite, the first equation is: c/2 + 3p + 10w = 100 Otherwise you'd have to sell some pigs or cows  April 13th, 2014, 03:39 PM #4 Newbie   Joined: Apr 2014 From: Texas Posts: 2 Thanks: 0 So it doesn't appear that you can completely solve the equation without plugging in numbers to see what gives you a whole number for ALL animals. That's basically how I solved it the first time, because you have two parameters you have to satisfy, 100 total animals and 100 dollars. April 13th, 2014, 08:40 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra No, you have two equations for three variables, so there's some trial and error to it. On the other hand, we know that $c$, $p$ and $w$ are all integers. And we can easily see that $0 \le w \le 10$, $0 \le p \le 33$ and so $57 \le c \le 200$. Furthermore, $c$ is even. Some of these are pretty simply to discount too ($w \gt 5$ does't allow us to reach 100 animals, for example). So we have a good number of constraints that limit our choices. Even better, we can calculate both $c$ and $p$ in terms of $w$, giving a very limited number of choices to verify. Thanks from Darkwing Tags problem, word Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post swm06 Algebra 9 March 13th, 2013 03:37 PM mathkid Calculus 5 October 20th, 2012 01:04 PM hemidol Algebra 2 April 8th, 2012 07:22 PM hannah2329 Algebra 1 September 19th, 2011 02:20 PM captonion Algebra 6 June 24th, 2010 09:28 AM

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