Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class taken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal. Let C represent the number of classes a customer takes.
Provide an inequality and the minimum number of classes a customer can take for Rebekah to meet her goal.

Answers:

The inequality is

The minimum number of classes a customer can take is 6 classes

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Explanation:

The expression 12C+35 represents how much a customer spends when they take C number of classes. The C is a placeholder for any positive whole number.

For instance, if they take C = 2 classes, then they spend 12*C+35 = 12*2+35 = 59 dollars.

Or if they take C = 3 classes, then they spend 12*C+35 = 12*3+35 = 71 dollars and so on.

We could try various values of C to find when 12C+35 is 100 or larger.

Or we can use algebra as shown in the next section.

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Because C is a positive whole number, we round up from 5.4167 to 6

We would not round to 5 even though 5.4167 is closer to 5 (hence the phrasing round up, instead of simple rounding).

If the customer took C = 5 classes, then they spend 12*C+35=12*5+35 = 95 dollars which is 5 short of the goal

But if they take C = 6 classes, then we're over the goal because 12*C+35 = 12*6+35 = 107. Larger values of C will result in larger total costs.

So the minimum number of classes a customer can take is 6 classes and this will allow Rebekah to reach her goal of $100 or more.

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