Answers:
The inequality is [tex]12C+35 \ge 100[/tex]
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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[tex]12C+35 \ge 100\\\\12C \ge 100-35\\\\12C \ge 65\\\\C \ge \frac{65}{12}\\\\C \ge 5.4167 \ \text{ (approximate)}\\\\[/tex]
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.
