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Video: Solving Word Problem Involving Percentages

Bethani Gasparine

On a train, 32 out of 50 seats are occupied. What percentage of seats are occupied and what percentage are empty?

02:38

Video Transcript

On a train, 32 out of 50 seats are occupied. What percentage of seats are occupied and what percentage are empty?

A percent is a ratio or fraction that compares a number to 100. So π‘₯ over 100 is taking π‘₯ and comparing it to 100. Now for our example, it says 32 out of 50 seats are occupied. We can create a proportion to compare them and solve for π‘₯, and then we will have our percentage.

So we take 32 out of 50 and by setting it equal to π‘₯ over 100, we’re able to write 32 out of 50 as a percentage. So our first step, we need to cross multiply; we need to find the cross product. So 50 times π‘₯ is equal to 100 times 32. Now we multiply. 50 π‘₯ is equal to 3200. Now to solve for π‘₯, we need to divide both sides by 50. Therefore, π‘₯ equals 64. So what does that mean? This means 64 out of 100 seats are considered occupied. So how many out of 100 seats will actually be empty? Well, we would take 100 and take away the 64 that are occupied, and then the remaining would be the seats that are empty. Therefore, 100 minus 64 is equal to 36. There would be 36 empty seats.

So our final step is we need to change these fractions into percentages. And the way that we do that is 64 out of 100 we can divide, which is .64 or 64 percent. So how many are empty? .36 or 36 percent. Let’s write this altogether as our final answer.

64 percent of the seats are occupied, and 36 percent of the seats are empty. Therefore, 64 plus 36 makes the full 100 percent which will be all of the people on the train.