✨Kevin D. Martin, PMP, ACP, CPM, LSSGB, Alamo PMI Founder ✨’s Post

Welcome to Week 5 of "What's The Answer Wednesday"! This week, we solved the equation 5X - 7 = 18. We explored isolating variables and balancing equations. After some quick steps, we found that X equals 5! Got a math question? Submit it, and you might see it featured next! #MathNMore #LearnWithUs #MathQuestions #WhatsTheAnswer

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🔍 Mathematical Exploration: Positive Integer Solutions for a, b, c, and d 🔍 Dear LinkedIn Community, I recently tackled an intriguing mathematical problem introduced by Doddy Kastanya and would love to share it along with the rich discussions that emerged. The challenge is to find positive integers a, b, c, and d that satisfy these equations: ab + cd = 69 ac + bd = 63 ad + bc = 57 The insightful exchanges in the comments significantly deepened our understanding and uncovered multiple solutions. 💡 Highlights from the Discussion: 1. Iterative Technique: One approach suggested by Lonny Thompson involved iterating through values from 1 to 20 for each variable, resulting in the following solutions:   a = 3, b = 5, c = 6, d = 9   a = 5, b = 3, c = 9, d = 6   a = 6, b = 9, c = 3, d = 5   a = 9, b = 6, c = 5, d = 3 Each solution also satisfies the constraint a + b + c + d = 23. 2. Analytical Approach: Conversion from Sum to Difference The equations are subtracted from each other to get three different equations in the form of product of difference terms. There are four ways to set the values for (a−c), (b−d), (a−d), and (b−c) based on the factors of 12 (-3,-4) and 6(-1,-6). For example as shown in https://lnkd.in/d_T_wPiM or in my comment following this post: Setting a-c = -4, b-d = -3, a-d = -1, and b-c = -6 yields (a, b, c, d) = (5, 3, 9, 6). However, there are three additional valid configurations: a−c=−3, b−d=−4, a−d=−1, b−c=−6 a−c=−4, b−d=−3, a−d=−6, b−c=−1 a−c=−3, b−d=−4, a−d=−6, b−c=−1 These different configurations produce the additional solutions identified through the iterative method explained in part (1). 3. Transformative Insight: all-negative versus all-positive solution set Reinterpreting the equations as (-a)(-b) + (-c)(-d) = 69, (-a)(-c) + (-b)(-d) = 63, and (-a)(-d) + (-b)(-c) = 57 and introducing variables a_tilde= -a, b_tilde = -b, c_tilde = -c, and d_tilde = -d simplifies the problem. This approach negates the all-negative solution set if any, thus providing positive integers for the solution set. The collaboration in the comments was incredibly valuable, showcasing diverse methods and deepening our collective understanding. It’s a testament to the power of shared knowledge and cooperative problem-solving. If possible I would like to encourage everyone to explore this problem and share any additional insights or alternative strategies. Your contributions are essential for building a vibrant and engaging mathematical community. Let’s continue to learn, share, and grow together! #Mathematics #ProblemSolving #Collaboration #Learning #MathChallenge #Community https://lnkd.in/d_T_wPiM https://lnkd.in/dJFkxTAG

Learn about rotation in math with our easy-to-follow guide! 💡 Visit our blog to explore definitions, examples & more: 🔗 bit.ly/3Ow371j. #Mathnasium #MathIsFun #MathTutor

To crack math word problems like this, start by identifying the clues: DIFFERENCE reveals how far apart the numbers are. SUM tells you their total when combined. By setting up equations based on these clues, you are already more than two steps closer to uncovering the mystery numbers! #MathematicsMadeSimple #ProblemSolvingSkills #MathTutoring #STEMEducation #CriticalThinking

This is an original mathematical card effect that is based on principles taught on the Absolute Math Magic channel: https://lnkd.in/g7PVUZRK Here are the videos referenced in this presentation: The Face Up Cards Principle https://lnkd.in/g5Zh5dgQ The Charlier Shuffle https://lnkd.in/ghwS3tvU ----------------

interesting math question, independent answer, didnt refer to any solution :)

Learn about rotation in math with our easy-to-follow guide! 💡 Visit our blog to explore definitions, examples & more: 🔗 bit.ly/3Ow371j. #Mathnasium #MathIsFun #MathTutor

An Original Card Effect Using the Under-Down Shuffle and Principles Taught on the Absolute Math Magic Channel: https://lnkd.in/g7PVUZRK Bessey Shuffle Diagrams https://lnkd.in/gU6SwfNC Bessey Sequences & Quasi-Bessey Sequences https://lnkd.in/g4kWvhMF ---------------

TIME FOR A MATH BREAK A short pause to continue thinking about the following two questions (see figure): 1/Do you agree with this quick and simple answer? 2/what is the value of the angle indicated with "?"