Question

There are red cars and blue cars in the parking lot. The ratio of blue to red is 11:6. There are 317 blue cars. How many red cars are in the parking lot?
172
173
581
53

Answer 1

Given the ratio of blue to red cars is \( 11:6 \), we know that for every 11 blue cars, there are 6 red cars.

Let \( b \) represent the number of blue cars and \( r \) represent the number of red cars. According to the information given:

\[
\frac{b}{r} = \frac{11}{6}
\]

From this ratio, we can express the number of red cars in terms of the number of blue cars:

\[
r = \frac{6}{11} b
\]

We are given that there are 317 blue cars. Plugging this value into the equation:

\[
r = \frac{6}{11} \times 317
\]

Now, calculating \( r \):

\[
r = \frac{6 \times 317}{11}
\]

Calculating \( 6 \times 317 \):

\[
6 \times 317 = 1902
\]

Now divide 1902 by 11 to find \( r \):

\[
r = \frac{1902}{11} = 173
\]

So, the number of red cars in the parking lot is \( \boxed{173} \).