At a concert 40% of the audience are children.One third of the rest of the audience are men.There are 120 women in the audience.Work out the total number of people in the audience.

Sure, let's break it down:

1. We know that 40% of the audience are children. This means that 60% of the audience are adults (100% - 40%).

2. We also know that one third of the adults are men. This means that two thirds of the adults are women.

3. We are told that there are 120 women in the audience.

4. Since two thirds of the adults are women, we can set up the equation 2/3 * (total number of adults) = 120. Solving for the total number of adults, we get 180.

Sure, let's solve this step by step:

1. We know that 40% of the audience are children. This means that 60% of the audience are adults (100% - 40% = 60%).

2. We also know that one third of the adults are men. This means that two thirds of the adults are women.

3. We are told that there are 120 women in the audience. Since two thirds of the adults are women, we can set up the equation 2/3 * (total number of adults) = 120.

4. Solving this equation for the total number of adults gives us (120 * 3) / 2 = 180 adults.

5. Since 60% of the audience are adults, we can set up the equation 0.6 * (total number of people in the audience) = 180.

6. Solving this equation for the total number of people in the audience gives us (180 / 0.6) = 300 people.

So, there are 300 people in the audience.