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For spring semester 2009, a college charged $\$ 40$ per unit (credit or hour) for tuition. All students paid a $\$ 3$ student representation fee each semester. Students who drove to school paid a $\$ 50$ parking fee each semester. Let T be the total one-semester cost (in dollars) of tuition and fees for a student who drove to school and took u units of classes. Answer parts (a) and (b).
a. Find an equation for $u$ and $T$. [Hint If there is trouble finding the equation, try creating a table of values for $u$ and $T$.]
The equation that describes the relationship between $T$ and $u$ is $T=$
(Simplify your answer. Type an expression using u as the variable.)
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Final Answer: The equation that describes the relationship between T and u is \(\boxed{T = 40u + 53}\).
Step 1 ：The total cost T is composed of three parts: the cost per unit, the student representation fee, and the parking fee. The cost per unit is variable and depends on the number of units u a student takes. The student representation fee and the parking fee are fixed costs that do not depend on the number of units. Therefore, the total cost T can be calculated as the sum of these three costs.
Step 2 ：The cost per unit is \(40 * u\), the student representation fee is \(3\), and the parking fee is \(50\). Therefore, the total cost T is \(40u + 3 + 50\).
Step 3 ：Final Answer: The equation that describes the relationship between T and u is \(\boxed{T = 40u + 53}\).
