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At an arts festival, a camp counselor bought food tickets for her hungry campers. The campers can use them to get hot dogs, which cost 44 tickets apiece, and burgers, which cost 33 tickets apiece. In total, the campers can use up to 3232 tickets, which is how many the counselor bought.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of hot dogs\newliney=y = the number of burgers\newlineChoices:\newline(A) 4x+3y≤324x + 3y \leq 32\newline(B) 3x+4y≤323x + 4y \leq 32\newline(C) 3x×4y≤323x \times 4y \leq 32\newline(D) 4x×3y≤324x \times 3y \leq 32

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Q. At an arts festival, a camp counselor bought food tickets for her hungry campers. The campers can use them to get hot dogs, which cost 44 tickets apiece, and burgers, which cost 33 tickets apiece. In total, the campers can use up to 3232 tickets, which is how many the counselor bought.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of hot dogs\newliney=y = the number of burgers\newlineChoices:\newline(A) 4x+3y≤324x + 3y \leq 32\newline(B) 3x+4y≤323x + 4y \leq 32\newline(C) 3x×4y≤323x \times 4y \leq 32\newline(D) 4x×3y≤324x \times 3y \leq 32
  1. Determine Cost and Budget: Determine the cost per item and the total budget in tickets.\newlineCost per hot dog: 44 tickets\newlineCost per burger: 33 tickets\newlineTotal tickets available: 3232\newlineWe need to find an inequality that represents the maximum number of hot dogs (x)(x) and burgers (y)(y) that can be bought with the available tickets.
  2. Write Inequality: Write the inequality based on the cost per item and the total budget.\newlineThe total cost for xx hot dogs is 4x4x tickets, and the total cost for yy burgers is 3y3y tickets. The sum of these costs cannot exceed the total number of tickets available, which is 3232.\newlineSo, the inequality will be: 4x4x (cost for hot dogs) + 3y3y (cost for burgers) ≤32\leq 32 (total tickets).
  3. Check Against Choices: Check the inequality against the given choices.\newlineWe have the inequality 4x+3y≤324x + 3y \leq 32. Now we need to match this inequality with the given choices.\newline(A) 4x+3y≤324x + 3y \leq 32\newline(B) 3x+4y≤323x + 4y \leq 32\newline(C) 3x×4y≤323x \times 4y \leq 32\newline(D) 4x×3y≤324x \times 3y \leq 32\newlineThe correct inequality that matches our calculation is choice (A).

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