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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) 265(f+8)=305265(f + 8) = 305\newline(B) 265f+8=305265f + 8 = 305\newline(C) 8(f+265)=3058(f + 265) = 305\newline(D) 8f+265=3058f + 265 = 305\newlineHow much did each favor cost?\newline____ $\$

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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) 265(f+8)=305265(f + 8) = 305\newline(B) 265f+8=305265f + 8 = 305\newline(C) 8(f+265)=3058(f + 265) = 305\newline(D) 8f+265=3058f + 265 = 305\newlineHow much did each favor cost?\newline____ $\$
  1. Understand the problem: Understand the problem.\newlineEstelle's party package costs $265\$265 without favors. With favors for 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 party package plus the total cost of the favors equals the total cost. The total cost of the favors is the cost per favor times the number of favors 88. So the equation is:\newlineCost of package + (Cost per favor ×\times Number of favors) = Total cost\newline265+(f×8)=305265 + (f \times 8) = 305
  3. Identify the correct equation: Identify the correct equation from the choices.\newlineLooking at the choices given, we need to find the one that matches the equation we set up in Step 22. The correct equation is:\newline(D) 8f+265=3058f + 265 = 305
  4. Solve for f: Solve the equation for f.\newlineSubtract 265265 from both sides of the equation to isolate the term with ff.\newline8f+265265=3052658f + 265 - 265 = 305 - 265\newline8f=408f = 40\newlineNow, divide both sides by 88 to solve for ff.\newlinef=40/8f = 40 / 8\newlinef=5f = 5