Rafael counted a total of 40 white cars and yellow cars. There were 9 times as, many white cars as yellow cars. How many white cars are there?

Let's define the variables for this problem:

- Let \( y \) represent the number of yellow cars.
- Let \( w \) represent the number of white cars.

From the problem, we have two key pieces of information:

1. The total number of cars (white and yellow) is 40. This gives us the equation:
   \[
   w + y = 40
   \]

2. There are 9 times as many white cars as yellow cars. This gives us the equation:
   \[
   w = 9y
   \]

Now, we can substitute the expression for \( w \) from the second equation into the first equation.

Substitute \( w = 9y \) into \( w + y = 40 \):

\[
9y + y = 40
\]

Combine like terms:

\[
10y = 40
\]

Now, solve for \( y \):

\[
y = \frac{40}{10} = 4
\]

So, there are 4 yellow cars.

Now, we use the equation \( w = 9y \) to find the number of white cars:

\[
w = 9 \times 4 = 36
\]

Thus, there are **36 white cars**.

### Summary

- Number of yellow cars, \( y = 4 \)
- Number of white cars, \( w = 36 \)

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

Here are some related questions to explore:

1. What if the ratio was 8 times as many white cars as yellow cars? How many of each would there be?
2. If there were 50 cars instead of 40, and still 9 times as many white cars as yellow cars, how many white cars would there be?
3. How would the solution change if there were 5 times as many white cars as yellow cars?
4. Can you create a general formula to find the number of white cars if you know the total number of cars and the ratio of white to yellow cars?
5. What happens if the total number of cars is a prime number and there is an integer ratio between the numbers of white and yellow cars?

**Tip:** When solving problems involving ratios, setting up equations based on the given relationships can simplify finding the solution.

Learn how to calculate the number of white cars when given a ratio problem involving yellow and white cars. This problem involves setting up and solving linear equations and understanding ratio relationships in algebra. Suitable for students in Grades 6-8.

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