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Math  /  Algebra

QuestionBookwork code: 5C Calculator allowed
A bowling alley can be hired for a party. The formula below shows the cost. A party cost £316£ 316. How many people were at the party?

Studdy Solution

STEP 1

1. The total cost of the party is £316.
2. The cost formula is given by: cost=£11×number of people+£30 \text{cost} = £11 \times \text{number of people} + £30 .
3. We need to find the number of people at the party.

STEP 2

1. Understand the cost formula.
2. Define a variable for the number of people.
3. Set up an equation using the given formula and total cost.
4. Solve the equation to find the number of people.

STEP 3

Understand the cost formula.
The formula given is: cost=£11×number of people+£30 \text{cost} = £11 \times \text{number of people} + £30
This means that the total cost is composed of a fixed cost of £30 plus £11 for each person attending the party.

STEP 4

Define a variable for the number of people.
Let n n be the number of people at the party.

STEP 5

Set up an equation using the given formula and total cost.
Substitute the total cost into the formula: £316=£11×n+£30 £316 = £11 \times n + £30

STEP 6

Solve the equation to find the number of people.
First, isolate the term with the variable by subtracting £30 from both sides: £316−£30=£11×n £316 - £30 = £11 \times n £286=£11×n £286 = £11 \times n
Now, divide both sides by £11 to solve for n n : n=£286£11 n = \frac{£286}{£11} n=26 n = 26
The number of people at the party is:
26 \boxed{26}

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