Video: Substitute Values into a Given Formula

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. What is the estimated amount of money, in dollars, collected by the toll collector on Monday during his 7-hour shift?

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Video Transcript

A tollbooth collects a 5-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. What is the estimated amount of money, in dollars, collected by the toll collector on Monday during his seven-hour shift?

We’re told in the question that the amount of money is equal to five π‘Ÿπ‘‡. π‘Ÿ is equal to the rate of cars passing the toll gate per hour. In this question, this is equal to 100 cars. 𝑇 is equal to the shift length. In this question, we know that the toll collector worked a seven-hour shift. This means that in order to calculate the estimated amount of money, we multiply five by 100 by seven. Multiplication is commutative. So we can multiply the numbers in any order. We will start by multiplying five by seven. This is equal to 35. 35 multiplied by 100 is equal to 3500.

The estimated amount of money taken by the toll collector is 3500 dollars.

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