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Zorluk: KolayAlgebraic Word Problems and Modeling

A bookstore sells hardcover books for $15\$15 each and paperback books for $10\$10 each. A customer purchased a total of 1212 books and spent $150\$150 in total. Let hh represent the number of hardcover books purchased and pp represent the number of paperback books purchased. Which of the following equations correctly model this situation? Select all such equations.

  1. h+p=12h + p = 12Cevap
  2. 15h+10p=15015h + 10p = 150Cevap
  3. 3h+2p=303h + 2p = 30Cevap
  4. D
    10h+15p=15010h + 15p = 150
  5. E
    15h+10p=1215h + 10p = 12

Cevap

The correct equations are h+p=12h + p = 12, 15h+10p=15015h + 10p = 150, and 3h+2p=303h + 2p = 30.
The system of equations that models this situation requires one equation for the total count of books (h+p=12h + p = 12) and one for the total monetary expenditure (15h+10p=15015h + 10p = 150). Dividing the cost equation 15h+10p=15015h + 10p = 150 by 5 gives another mathematically equivalent relation 3h+2p=303h + 2p = 30. Thus, all three of these statements accurately represent the given conditions.

Adım Adım Çözüm

1
Formulate the total quantity equation
h+p=12h + p = 12
The total number of books bought is 12, which is the sum of hardcover books hh and paperback books pp.
2
Formulate the total cost equation
15h+10p=15015h + 10p = 150
Hardcover books cost $15\$15 each and paperbacks cost $10\$10 each, yielding a total cost of $150\$150.
3
Simplify the total cost equation by dividing by the greatest common divisor
3h+2p=303h + 2p = 30
Dividing all coefficients in 15h+10p=15015h + 10p = 150 by 55 produces an equivalent simplified linear equation.

Anahtar Kavram

Linear Modeling and Equivalent Equations
Tahmini Süre:1m 0s
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Konular

Algebraic Word Problems and Modeling

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