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Let's solve the problem step by step.

### Problem Summary:
- Total parking spaces: 200
- 10% of the spaces are for staff.
- The remaining spaces are for disabled people, parents, and other customers in the ratio \( 1 : 2 : 7 \).
- Paul is painting signs only for staff, disabled people, and parents.

### Step 1: Calculate the number of spaces for staff.
Since 10% of the spaces are for staff:
\[
\text{Staff spaces} = 10\% \text{ of } 200 = 0.1 \times 200 = 20
\]

### Step 2: Calculate the remaining spaces.
The remaining spaces after allocating for staff:
\[
\text{Remaining spaces} = 200 - 20 = 180
\]

### Step 3: Distribute the remaining spaces according to the ratio \( 1 : 2 : 7 \).
The ratio can be expressed as:
\[
1x + 2x + 7x = 10x
\]
where \( x \) is a common factor.

So, 
\[
10x = 180 \quad \Rightarrow \quad x = \frac{180}{10} = 18
\]

This gives:
- Spaces for disabled people: \( 1x = 18 \)
- Spaces for parents: \( 2x = 36 \)
- Spaces for other customers: \( 7x = 126 \)

### Step 4: Calculate the total number of spaces Paul is going to paint a sign for.
Paul is painting signs for staff, disabled people, and parents:
\[
\text{Total spaces to paint signs for} = 20 \, (\text{staff}) + 18 \, (\text{disabled}) + 36 \, (\text{parents}) = 74
\]

**Answer:** Paul is going to paint signs for **74** spaces.

Would you like any additional details or have any questions?

Here are five related questions to expand on the concepts:
1. How would the number of spaces change if the ratio for disabled, parents, and other customers was \( 2:3:5 \)?
2. If the total number of spaces increased to 300, how many spaces would Paul need to paint signs for?
3. How would you calculate the number of spaces for staff if 15% of the spaces were allocated to them instead of 10%?
4. What would happen to the total number of spaces Paul is painting signs for if he included the other customers as well?
5. Can you determine the percentage of the total parking spaces that Paul is painting signs for?

**Tip:** When dealing with ratios, always break them down into their simplest form to distribute quantities effectively.

A supermarket car park has 200 spaces. 10% of the spaces are for staff. The other spaces are for disabled people, for parents, and for other customers in the ratio 1:2:7. Paul is going to paint a sign for each of the spaces for staff, for disabled people, and for parents. He is not going to paint signs for the spaces for other customers. Work out the total number of spaces Paul is going to paint a sign for.

Solve a supermarket car park problem involving 200 spaces with percentage and ratio distribution. Learn how to calculate the number of parking spaces for staff, disabled people, and parents. Suitable for students in Grades 6-8.

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