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A publishing company prints newspapers and magazines.\newlineLet NN represent the number of newspapers and MM represent the number of magazines the company can print with its daily supply of ink cartridges.\newline0.5N+2.5M60000.5N + 2.5M \leq 6000\newlineThe company wants to print 80008000 newspapers daily. How many magazines at most can the company print daily with the remaining number of ink cartridges?\newlineChoose 11 answer:\newline(A) The company can print 800800 magazines at most.\newline(B) The company can print 25002500 magazines at most.\newline(C) The company can print 60006000 magazines at most.\newline(D) The company can print 80008000 magazines at most.

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Q. A publishing company prints newspapers and magazines.\newlineLet NN represent the number of newspapers and MM represent the number of magazines the company can print with its daily supply of ink cartridges.\newline0.5N+2.5M60000.5N + 2.5M \leq 6000\newlineThe company wants to print 80008000 newspapers daily. How many magazines at most can the company print daily with the remaining number of ink cartridges?\newlineChoose 11 answer:\newline(A) The company can print 800800 magazines at most.\newline(B) The company can print 25002500 magazines at most.\newline(C) The company can print 60006000 magazines at most.\newline(D) The company can print 80008000 magazines at most.
  1. Understand given inequality: Understand the given inequality and what it represents.\newlineThe inequality 0.5N+2.5M60000.5N + 2.5M \leq 6000 represents the maximum number of newspapers (N)(N) and magazines (M)(M) the company can print with its daily supply of ink cartridges. The coefficients 0.50.5 and 2.52.5 represent the amount of ink used per newspaper and per magazine, respectively.
  2. Substitute newspapers into inequality: Substitute the given number of newspapers into the inequality.\newlineThe company wants to print 80008000 newspapers daily. We substitute N=8000N = 8000 into the inequality:\newline0.5×8000+2.5M60000.5 \times 8000 + 2.5M \leq 6000
  3. Perform multiplication for newspapers: Perform the multiplication to find the amount of ink used for the newspapers.\newline0.5×8000=40000.5 \times 8000 = 4000\newlineSo the inequality becomes:\newline4000+2.5M60004000 + 2.5M \leq 6000
  4. Subtract ink used for newspapers: Subtract the amount of ink used for the newspapers from the total ink available.\newlineTo find out how much ink is left for printing magazines, we subtract 40004000 from both sides of the inequality:\newline4000+2.5M4000600040004000 + 2.5M - 4000 \leq 6000 - 4000\newlineThis simplifies to:\newline2.5M20002.5M \leq 2000
  5. Divide to solve for magazines: Divide both sides of the inequality by the coefficient of MM to solve for MM.\newlineTo find the maximum number of magazines the company can print, we divide both sides by 2.52.5:\newline2.5M2.520002.5\frac{2.5M}{2.5} \leq \frac{2000}{2.5}\newlineThis simplifies to:\newlineM800M \leq 800

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