Dan is planning a fancy dinner for his friend's birthday. Heirloom Café charges $21 per person for the meal, plus an additional $8 per person for dessert. Hot Stone Bakery charges $26 per person for the meal, plus $33 for a birthday cake the friends can share. Which equation can you use to find p, the number of people who would need to come to the dinner for the two restaurants to cost the same? Choices: (A)26p + 8 = 21p + 33 (B)21p + 8p = 26p + 33 How many people would need to come to the dinner for the two restaurants to cost the same? ____ people

Question

Dan is planning a fancy dinner for his friend's birthday. Heirloom Café charges $21 per person for the meal, plus an additional $8 per person for dessert. Hot Stone Bakery charges $26 per person for the meal, plus $33 for a birthday cake the friends can share. Which equation can you use to find p, the number of people who would need to come to the dinner for the two restaurants to cost the same?   Choices: (A)26p + 8 = 21p + 33 (B)21p + 8p = 26p + 33  How many people would need to come to the dinner for the two restaurants to cost the same?   ____ people

Bytelearn · Accepted Answer

Set Up Equation: Let's first set up the equation for the cost of the dinner at Heirloom Café. The cost per person is $21 for the meal plus $8 for dessert, so the total cost for p people would be: Cost at Heirloom Café = 21p + 8pCost Calculation: Now, let's set up the equation for the cost of the dinner at Hot Stone Bakery. The cost per person is $26 for the meal, and there is an additional $33 for the birthday cake that everyone can share, so the total cost for p people would be: Cost at Hot Stone Bakery = 26p + 33Equation Correction: To find the number of people needed for the two restaurants to cost the same, we set the two cost equations equal to each other: 21p + 8p = 26p + 33However, we made a mistake in the previous step. The cost for dessert at Heirloom Café is a flat $8 per person, not a one-time fee. The correct equation should be: 21p + 8 = 26p + 33

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