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Scavenger+Hunt PREVIOUS ANSWER: SYSTEMS WORD PROBLEMS 13 Scavenger Hunt The local bookstore is having a sale on used books. Nate bought 3 hardcover books and 7 paperback books and spent $29.50. Tia bought 2 hardcover books and 5 paperback books and spent $20.50. What is the cost of a hardcover book?

Scavenger+Hunt\newlinePREVIOUS ANSWER:\newlineSYSTEMS WORD PROBLEMS\newline1313 Scavenger Hunt\newlineThe local bookstore is having a sale on used books. Nate bought 33 hardcover books and 77 paperback books and spent $29.50 \$ 29.50 . Tia bought 22 hardcover books and 55 paperback books and spent $20.50 \$ 20.50 . What is the cost of a hardcover book?

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Q. Scavenger+Hunt\newlinePREVIOUS ANSWER:\newlineSYSTEMS WORD PROBLEMS\newline1313 Scavenger Hunt\newlineThe local bookstore is having a sale on used books. Nate bought 33 hardcover books and 77 paperback books and spent $29.50 \$ 29.50 . Tia bought 22 hardcover books and 55 paperback books and spent $20.50 \$ 20.50 . What is the cost of a hardcover book?
  1. Define Variables: Let's call the cost of a hardcover book HH and the cost of a paperback book PP. Nate's purchase gives us the equation 3H+7P=29.503H + 7P = 29.50.
  2. Form Equations: Tia's purchase gives us another equation, 2H+5P=20.502H + 5P = 20.50.
  3. Multiply Second Equation: Now we have a system of equations:\newline11) 3H+7P=29.503H + 7P = 29.50\newline22) 2H+5P=20.502H + 5P = 20.50\newlineLet's multiply the second equation by 1.51.5 to line up the PP terms with the first equation.
  4. Correct Multiplication: After multiplying we get:\newline1.5(2H)+1.5(5P)=1.5(20.50)1.5(2H) + 1.5(5P) = 1.5(20.50)\newlineWhich simplifies to:\newline3H+7.5P=30.753H + 7.5P = 30.75\newlineOops, we should have multiplied by 1.51.5 to get 7P7P, not 7.5P7.5P.

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