Tech Math: Word Problems In A Linear System

 

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Relevant Material: "Applications of word problems in linear systems include finding a number based on its digits, calculating ages, and solving mixture problems like mixing saline solutions. They are also used for motion problems involving distance, rate, and time, such as calculating airplane or boat speeds, and for scenarios involving two different rates or costs, like those found in savings or production plans. 
Common applications
  • Age Problems: Use a system of equations to find the current and future ages of two people based on given information like the sum of their ages or a relationship between their ages.
  • Mixture Problems: Determine the amount of each component needed to achieve a desired final mixture with specific properties, such as mixing different concentrations of a solution to create a new solution with a target concentration.
  • Motion Problems: Solve for unknowns in distance, rate, and time scenarios (d = rt). This includes situations where objects are traveling with or against a current, like a boat, or against wind, like an airplane.
  • Cost and Rate Problems: Find unknown costs or rates based on different scenarios. This can involve finding the price of an item after a price increase or solving for the number of items or the time it takes to reach a specific financial goal, such as in a savings plan.
  • Digit and Number Problems: Identify an unknown number by setting up equations based on the sum of its digits and the value resulting from reversing the digits. 
Strategy for solving
  1. Identify variables: Assign variables to the unknown quantities in the problem.
  2. Create equations: Translate the information given in the word problem into a system of two linear equations using the variables.
  3. Solve the system: Use methods like substitution or elimination to solve for the variables.
  4. Answer the question: Ensure you answer all parts of the original question. For example, if the problem asks for an age and a number, make sure you find both.
  5. Check your work: Substitute your answers back into the original equations to verify that they are correct and make sense in the context of the problem.." (Google) 



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