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Amanda [17]
2 years ago
8

John goes to a bookstore. he wants to buy at. most 25 books and spend at most $75. paperback books cost 1.75 and har cover books

cost 2.50. create a system of linear inequalities that could be used to determine all the different combination of paperback and hardcover books he can purchase
Mathematics
1 answer:
Yanka [14]2 years ago
6 0

Answer:

  • x + y ≤ 25
  • 1.75x + 2.50y ≤ 75

Step-by-step explanation:

  • Paperback books = x
  • Hard cover books = y

<u>Number of books:</u>

  • x + y ≤ 25

<u>Cost of books:</u>

  • 1.75x + 2.50y ≤ 75

The system above is the one we need

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Answer:

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Step-by-step explanation:

The coefficients of x and y do not have any "nice" relations, so doing this by elimination is just "brute force" with no particular subtlety.

After multiplying by appropriate numbers, you want the coefficient of one of the variables in one equation to be the opposite of the coefficient of the same variable in the other equation. Here, we can get that by multiplying the first equation by 7 and the second equation by 2.

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Adding these equations with opposite x-coefficients eliminates the x-terms. (That is how the "elimination" method gets its name.)

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The solution is x = 1, y = -7.

_____

<em>Additional comment</em>

The multipliers used in this process are essentially the coefficients of one of the variables, with one of them negated. Here, we chose the x-coefficients, because negating one of them gives two positive multipliers. We judge it easier to do the arithmetic using positive numbers.

Had we chosen to use the y-coefficients (3 and 2) for our multipliers, we would probably multiply the first equation by 2, and the second equation by -3. That way, the remaining x-coefficient would be positive.

Planning ahead is helpful, but not essential. It can help to avoid errors and make the work easier to do.

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