Video: Solving Word Problem Involving Percentages

The graph shows the results poll of 4532 radio listeners. To the nearest whole number, how many more people listen to the radio in the gym than in the car?

03:37

Video Transcript

The graph shows the results poll of 4532 radio listeners to the nearest whole number. How many more people listen to the radio in the gym than in the car? The graph tells us that 42 percent of the listeners listen to the radio in the gym; 25 percent of the radio listeners listen to the radio in the car. This means that we can calculate the percentage difference by subtracting 25 percent from 42 percent. 42 minus 25 is equal to 17. Therefore, 17 percent more listeners listen to the radio in the gym than in the car. We were asked to calculate how many more people listen to the radio in the gym than in the car. This means that our answer will be equal to 17 percent of 4532.

The word percent means out of 100. Therefore, 17 percent is the same as 17 out of 100 or 17 100ths. This can also be written as a decimal as 0.17 as 17 divided by 100 is 0.17. The word of in maths means multiply. Therefore, we need to multiply 17 100ths by 4532. Alternatively, we can multiply 0.17 by 4532. Typing either of these into the calculator gives us an answer of 770.44. As we’re dealing with the number of people, we need to round this to the nearest whole number. The four after the decimal point is the deciding number. And as this is less than five, we’ll round down. 770.44 rounded to the nearest whole number is 770. This means that 770 more people listen to the radio in the gym than they do in the car.

An alternative method would have been to have worked out the number of people who listen to the radio in the gym and then, separately, the number of people that listen to radio in the car and subtracted our answers. We could work out how many people listen to the radio in the gym by multiplying 0.42 by 4532, alternatively multiplying 42 100ths by 4532. This is equal to 1903 people to the nearest whole number. Multiplying 0.25 by 4532 gives us the number of people that listen to the radio in the car. This is equal to 1133. 1903 minus 1133 is also equal to 770. We have once again proved that 770 more people listen to the radio in the gym than they do in the car.

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