Final answer:
To determine how many people must attend the dinner for both restaurants to cost the same, an equation was set up comparing the per-person cost at Heirloom Cafe ($29x) and Hot Stone Bakery ($26x + $33). Solving the equation $29x = $26x + $33 shows that 11 people need to attend.
Step-by-step explanation:
To find out how many people would need to come to the dinner for the two restaurants to cost the same, we need to set up an equation. Let's let x represent the number of people.
- Heirloom Cafe: The cost per person is $21 for the meal and $8 for dessert, making it $21 + $8 = $29 per person. So the total cost is $29x.
- Hot Stone Bakery: The cost per person is $26 for the meal, and the birthday cake is a one-time cost of $33, regardless of the number of people. The total cost is $26x + $33.
We want these two costs to be equal, so we set them up in an equation: $29x = $26x + $33.
Now, solve for x:
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- Subtract $26x from both sides to get: $29x - $26x = $33.
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- This simplifies to $3x = $33.
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- Divide both sides by $3 to get x = $33 / $3.
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- Solving this gives x = 11.
Therefore, 11 people would need to come to the dinner for the two restaurants to cost the same.