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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) 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) 265f+8=305265f + 8 = 305 \newline(B) 265(f+8)=305265(f + 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. Identify variables: Understand the problem and identify the variables. Estelle's basic party package costs $265\$265. She added favors for each of her 88 guests, which increased the total cost to $305\$305. We need to find the cost of each favor, which we will call ff.
  2. Set up equation: Set up the equation based on the information given.\newlineThe total cost of the party is the sum of the basic package cost and the cost of the favors for all guests. The equation should reflect this relationship.
  3. Choose correct equation: Choose the correct equation from the given choices.\newlineThe basic package cost is $265\$265, and the cost of favors for 88 guests is 88 times the cost of one favor (8f)(8f). The total cost is $305\$305. So the equation is the basic package cost plus the cost of all favors equals the total cost: 265+8f=305265 + 8f = 305.\newlineThe correct equation is (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 find ff.\newline8f8=408\frac{8f}{8} = \frac{40}{8}\newlinef=5f = 5