The ratio of men to women on a bus is 5:9. If the total number of passengers on the bus is 84, and 20 women alight from the bus at the next stop, how many women have remained on the bus?

Step 1: Define variables for the initial number of men and women

We are given that the ratio of men to women is 5:9. This means that for some common multiplier $x$, the number of men can be represented as $5x$ and the number of women as $9x$.

Step 2: Set up an equation for the total number of passengers

The total number of passengers on the bus initially is 84. This total is the sum of the number of men and the number of women.

Step 3: Solve for x

Combine the terms on the left side of the equation and then divide to find the value of $x$. This value represents the common multiplier for the ratio.

Step 4: Calculate the initial number of men and women

Substitute the value of $x$ back into the expressions for the number of men and women to find their initial counts on the bus.

Step 5: Calculate the number of women remaining after some alight

Subtract the number of women who alighted from the bus from the initial number of women to find out how many women are left on the bus.

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