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Systems of Linear Equations Word Problems WorksheetTeacher’s Answer KeyA multiple choice test consists of 100 questions. A correct answer is worth 2 marks, while an incorrect answer is worth -1 marks. If a student receives a score of 80, how many questions did this student answer incorrectly? (40 questions)Let x = # of incorrect answers, and y = # of correct answers.y + x = 1002y – x = 80So y = 60 and x = 40. White chocolate costs $2.00 per bar, and dark chocolate costs $2.50 per bar. If you buy 15 bars of chocolate for $34 dollars, how many bars of dark chocolate did you buy? (8 bars)Let w = # of white chocolate bars, and d = # of dark chocolate barsw + d = 152w + 2.5d = 34So d = 8 and w = 7A cellular company’s revenue and cost functions for selling mobile phones can be modelled by the linear equations R = 50n and C = 20n + 300, where R represents the revenue in dollars, C represents the cost, and n represents the number of phones sold. How many phones must this company sell in order to have no profit? (Profit = Revenue – Cost) (10 phones)To have no profit, we have 0 = Revenue – Cost, or equivalently, Revenue = Cost50n = 20n + 300So n = 10The sum of two numbers is 17. The difference between the larger number and the smaller number is 7. What is the value of the smaller number? (5) Let x = the first number, and y = the second number x + y = 17x – y = 7So x = 12 and y = 5. The smaller number is 5John has $5.05 in quarters and nickels in his pocket. If John only has 25 coins in his pocket, how many of the coins are quarters? (22 quarters)Let n = # of nickels, and q = # of quartersn + q = 250.05n + 0.25q = 5.05So n = 3 and q = 22A class of 32 consists of students who either have red or yellow shirts. If there are 12 more people with red shirts than there are people with yellow shirts, how many of the students have red shirts? (22 students)Let r = # of students with red shirt, and y = # of students with yellow shirtsr + y = 32r = y + 12So y = 10 and r = 22 ................
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