Video: Calculate a Percentage Increase

A tollbooth collects a $5 toll from every automobile passing by a certain road. The toll collector finds that during his shift, which lasts 𝑇 hours, the amount of money collected 𝑀, in dollars, can be estimated by the formula 𝑀 = 5π‘Ÿπ‘‡, where π‘Ÿ is the average number of cars passing per hour. On Monday, it is estimated that the rate of cars passing the toll gate is 100 cars per hour. On Tuesday, the rate of cars passing by the toll gate increases to 3 cars per minute. What is the percentage increase in the estimated amount of collected money by the toll collector during his 7-hour shift?

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Video Transcript

A tollbooth collects a five-dollar toll from every automobile passing by a certain road. The toll collector finds that during his shift, which lasts 𝑇 hours, the amount of money collected 𝑀, in dollars, can be estimated by the formula 𝑀 equals five π‘Ÿπ‘‡, where π‘Ÿ is the average number of cars passing per hour. On Monday, it is estimated that the rate of cars passing the toll gate is 100 cars per hour. On Tuesday, the rate of cars passing by the toll gate increases to three cars per minute. What is the percentage increase in the estimated amount of collected money by the toll collector during his seven-hour shift?

We are told in the question that the amount of money can be estimated using the formula 𝑀 is equal to five π‘Ÿπ‘‡. The five is the amount of money paid by every automobile. The π‘Ÿ is the number of cars per hour. The 𝑇 is equal to the length of the shift. In this question, the toll collector works a seven-hour shift. The only variable that alters between Monday and Tuesday is the number of cars that passes the tollbooth. On Monday, there are 100 cars that pass per hour. Whereas on Tuesday, we are told that three cars pass per minute.

We know that 60 minutes is equal to one hour. Therefore, we can calculate the number of cars that pass per hour on Tuesday by multiplying three by 60. This is equal to 180. The number of cars that pass per hour on Tuesday is 180. To calculate a percentage increase, we need to divide the actual increase by the original value and then multiply this by 100, as percentages are out of 100.

The actual increase in cars per hour is 80, as 180 minus 100 is 80. The original value is 100, as this was the number of cars that passed on Monday. We need to multiply 80 over 100 by 100. As we’re both dividing and multiplying by 100, these cancel. This leaves us with a value of 80 percent. As the expected number of cars increases by 80 percent, the estimated amount of collected money will also increase by 80 percent.

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