Video: Using Percentages and Multipliers to Solve an Equation

To obtain a driver’s license, you need to pass a written test and then pass a practical driving test. In May, 𝑛 people attempted to obtain a driver’s license from a particular branch of the Department of Motor Vehicles. 90% of these people passed the written test. 30% of those who passed the written test also passed the practical driving test. The number of people who passed both tests was 4050. What is the value of 𝑛?

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Video Transcript

To obtain a driver’s license, you need to pass a written test and then pass a practical driving test. In May, 𝑛 people attempted to obtain a driver’s license from a particular branch of the Department of Motor Vehicles. 90 percent of these people passed the written test. 30 percent of those who passed the written test also passed the practical driving test. The number of people who passed both tests was 4050. What is the value of 𝑛?

We’re told in the question that 𝑛 people attempted to obtain a driver’s license. 90 percent of these people passed the written test. 90 percent can be written as a decimal as 0.9. Therefore, 0.9𝑛 people passed the written test. 30 percent of those who passed the written test also passed the practical test. As 30 percent is the same as 0.3, we could calculate the number of people who passed both tests by multiplying 0.3 by 0.9𝑛.

Three multiplied by nine is equal to 27. Therefore, 0.3 multiplied by 0.9 is equal to 0.27. This means that an expression for the number of people who passed both tests is 0.27𝑛.

We are also told in the question that this number is equal to 4050. We can therefore write the equation 0.27𝑛 is equal to 4050. To calculate the value of 𝑛, we can divide both sides by 0.27. On the left-hand side, we’re just left with 𝑛. 4050 divided by 0.27 is equal to 15000. We can therefore say that the value of 𝑛, the number of people who attempted to obtain a driver’s license in May, is 15000.

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