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The formula given for the cost of the party is:

\[
\text{cost} = 11 \times (\text{number of people}) + 30
\]

We are told that the total cost for the party is £316. Let's solve for the number of people:

\[
316 = 11 \times (\text{number of people}) + 30
\]

First, subtract 30 from both sides:

\[
316 - 30 = 11 \times (\text{number of people})
\]
\[
286 = 11 \times (\text{number of people})
\]

Now, divide both sides by 11:

\[
\text{number of people} = \frac{286}{11} = 26
\]

So, the number of people at the party is 26.

Would you like more details or have any questions about this?

Here are 5 related questions to deepen your understanding:
1. How would the cost change if there were 30 people at the party?
2. What would be the total cost if the base cost (£30) were removed?
3. If the bowling alley charged £15 per person instead of £11, how would the formula change?
4. How can we rearrange the formula to solve directly for the number of people based on the cost?
5. What if the fixed cost was different, say £50? How would this affect the calculations?

**Tip**: In formulas involving cost, always check if there's a fixed charge (like the £30 here) and account for it first before calculating the variable part!

A party cost £316. How many people were at the party if the formula for cost is £11 times the number of people plus £30?

Learn how to calculate the number of people at a party when the total cost is £316, using the formula £11 per person plus a fixed cost of £30. This example introduces basic algebra and linear equations suitable for students in Grades 6-8.

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