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Britt hires a personal trainer for the summer. The trainer charges 40 dollars for a sign-up fee plus 22.50 dollars per hour. If Britt spends a total of 940 dollars over the summer, how many hours did she train with the trainer?

Answer :

Final answer:

Britt spent 40 hours training with the personal trainer over the summer. This conclusion is reached by solving the given linear equation which relates cost to number of training hours.

Explanation:

To answer Britt's question, we need to use the concepts of linear equations since this is a problem of basic algebra. The cost equation for the personal trainer is in the form of y = mx + b, very similar to the situation Svetlana's tutoring charge in example 12.4. In this equation, y is the total cost, m is the hourly rate, x is the number of hours trained, and b is the initial sign up fee.

For Britt, the total cost for the summer (y) is $940. The hourly rate (m) is $22.50, and the sign-up fee (b) is $40. We don't know the number of hours (x), which is what we're trying to find.

So, we have: 940 = 22.5x + 40.

To solve for x, we first subtract 40 from both sides, which gives us 900 = 22.5x. Then we divide by 22.5, arriving at x = 900 / 22.5 = 40.

So, Britt trained with the trainer for 40 hours over the summer.

Learn more about Algebra here:

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