Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 October 9th, 2018, 06:22 PM #1 Newbie   Joined: Oct 2018 From: canada Posts: 1 Thanks: 0 Golf Balls! A worker is packaging 177 golf balls into sleeves. Each sleeve can hold 3 golf balls. There are two options for how many sleeves can be packaged into a box: The first type of box can hold 4 sleeves The second type of box can hold 5 sleeves How many boxes and of which type are needed to package all of the golf balls? (This problem is very simple to do using trial/error, but I'm looking for an algebraic solution) Thanks  October 9th, 2018, 06:43 PM #2 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,948 Thanks: 1139 Math Focus: Elementary mathematics and beyond Let f be the number of the first type of box and let s be the number of the second type of box. 12f + 15s = 177. By inspection, f = 1 and s = 11. I don't think there is enough information given to form a second equation relating boxes, balls and sleeves that isn't just a scalar multiple of the above equation. October 9th, 2018, 07:56 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2644 Math Focus: Mainly analysis and algebra Written as \begin{align}12(f+s)+3s &= 177 \\ 4(f+s) + s &= 59\end{align} We see that we require $f+s < 15$ and that we pick $s$ to complete the sum for an appropriate value of $(f+s)$. This gives rise to solutions $(f,s) \in \{ (11,3), (6,7), (1,11) \}$, being the solutions for $(f+s)$ equal to 14, 13 and 12 respectively. Lower values of $(f+s)$ don't have solutions as they require $s > f+s$ which implies negative values of $f$. Thanks from greg1313 Last edited by v8archie; October 9th, 2018 at 07:59 PM. Tags balls, golf 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 Loren Physics 4 August 10th, 2017 11:21 PM Skyer Algebra 3 January 6th, 2014 11:26 AM r-soy Physics 0 June 15th, 2012 04:21 AM byron123 Advanced Statistics 2 September 10th, 2008 09:39 AM

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