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)21p + 8p = 26p + 33 (B)26p + 8 = 21p + 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)21p + 8p = 26p + 33 (B)26p + 8 = 21p + 33  How many people would need to come to the dinner for the two restaurants to cost the same?   ____ people

Bytelearn · Accepted Answer

Set Equations Equal: To find the correct equation, we need to set the total cost for each restaurant equal to each other. For Heirloom Café, the cost per person is $21 for the meal plus $8 for dessert, which is a total of $21p + $8p per p people. For Hot Stone Bakery, the cost is $26 per person for the meal plus a flat $33 for the birthday cake, which is $26p + $33 for p people. The equation to find the point where the costs are the same is therefore: 21p + 8p = 26p + 33Combine Like Terms: Now we simplify the equation by combining like terms on the left side: (21p + 8p) = 26p + 33 29p = 26p + 33Isolate Variable: Next, we isolate the variable p by subtracting 26p from both sides of the equation: 29p - 26p = 26p + 33 - 26p 3p = 33Divide to Solve: Finally, we divide both sides by 3 to solve for p: 3p / 3 = 33 / 3 p = 11

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