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Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs 265265 $\$ and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her 88 guests, bringing the total to 305305 $\$.\newlineWhich equation can you use to find ff, the cost of each favor?\newlineChoices:\newline(A) 265f+8=305265f + 8 = 305\newline(B) 265(f+8)=305265(f + 8) = 305\newline(C) 8f+265=3058f + 265 = 305\newline(D) 8(f+265)=3058(f + 265) = 305\newlineHow much did each favor cost?\newline____ $\$

Full solution

Q. Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs 265265 $\$ and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her 88 guests, bringing the total to 305305 $\$.\newlineWhich equation can you use to find ff, the cost of each favor?\newlineChoices:\newline(A) 265f+8=305265f + 8 = 305\newline(B) 265(f+8)=305265(f + 8) = 305\newline(C) 8f+265=3058f + 265 = 305\newline(D) 8(f+265)=3058(f + 265) = 305\newlineHow much did each favor cost?\newline____ $\$
  1. Understand the problem: Understand the problem.\newlineEstelle's party package costs $265\$265, and after adding favors for each of her 88 guests, the total cost is $305\$305. We need to find the cost of each favor, represented by ff.
  2. Set up the equation: Set up the equation.\newlineThe cost of the favors is the difference between the total cost and the base cost of the package. The base cost is $265\$265, and the total cost with favors is $305\$305. The number of favors is 88, so the equation to find the cost of each favor is 8f+265=3058f + 265 = 305.
  3. Choose the correct equation: Choose the correct equation from the given choices.\newlineThe correct equation that represents the situation is (C)8f+265=305(C) 8f + 265 = 305.
  4. Solve for ff: Solve the equation for ff.\newlineSubtract 265265 from both sides of the equation to isolate the term with ff.\newline8f+265265=3052658f + 265 - 265 = 305 - 265\newline8f=408f = 40
  5. Divide to find ff: Divide both sides by 88 to find the value of ff.
    f=408f = \frac{40}{8}
    f=5f = 5