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Let the cost of a pencil be dollars and let the cost of a pen be dollars. Find the cost of a pencil and the cost of a pen. Word problems involving costsĪ certain store sells pencils and pens for 3 dollars, while pencils and pen are sold for 2 dollars. Since reversing the first and third digits increases the number by, we have that When the first and third digits are reversed, the number becomes, which is effectively. With this in mind, our original number is. To get the second equation, first note that any 3-digit number abc is actually. We’re already provided with the middle digit, so the number can take the form, where is the hundreds digit and is the ones digit. Find the 3-digit number, given that it’s middle digit is. If the first and third digits are reversed, the number increases by. The sum of the digits of a 3-digit number is. According to the question,, and so we have the linear system If we multiply by, we’ll have then if we subtract we’ll have. If he multiplies the smaller number by and then subtracts the bigger number, he gets. Word problems involving integers Example 1 In the examples below, our focus will be on step 4 (since we’ve already covered the three standard methods of solving linear systems: elimination, substitution, and graphing). solve the linear equations formulated in the previous step and interpret the solution.formulate two linear equations based on the information provided in the question (this is a crucial step, and is one of the reasons you should endeavour to understand the question).use letters to represent the two unknowns.
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identify the unknowns in the question (there will usually be two unknowns, since we’re dealing with linear systems in two variables).ensure that you understand the question.Technically, the question hasn’t changed it’s just the presentation or formulation - and the solver’s subsequent perception and interpretation - that may change.Īs and begin to have physical “meanings”, the class of problems that a single pair of equations can model can be many. What if the question was presented differently, in words, for example? It could be something like “ Find two numbers whose sum is and when the second number is subtracted from twice the first number gives ”. You will very easily accomplish this using any of the methods we considered before. If you are asked to solve the linear system