Questions: For spring semester 2009, a college charged 20 per unit (credit or hour) for tuition. All students paid a 1 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), (b), and (c).
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.)
Transcript text: For spring semester 2009, a college charged $\$ 20$ per unit (credit or hour) for tuition. All students paid a $\$ 1$ 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), (b), and (c).
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 $\mathrm{T}=\square$ $\square$
(Simplify your answer. Type an expression using $u$ as the variable.)
Solution
Solution Steps
To find the equation for \( T \) in terms of \( u \), we need to consider all the costs involved for a student who drives to school. The total cost \( T \) includes the cost per unit, the student representation fee, and the parking fee. The cost per unit is \( \$20 \), the student representation fee is \( \$1 \), and the parking fee is \( \$50 \). Therefore, the total cost \( T \) can be expressed as a function of the number of units \( u \).
Step 1: Define the Total Cost Equation
The total cost \( T \) for a student who drives to school and takes \( u \) units of classes can be expressed as:
\[
T = 20u + 1 + 50
\]
This simplifies to:
\[
T = 20u + 51
\]
Step 2: Calculate Total Cost for \( u = 5 \)
Substituting \( u = 5 \) into the equation:
\[
T = 20(5) + 51
\]
Calculating this gives:
\[
T = 100 + 51 = 151
\]
Final Answer
The total cost \( T \) when \( u = 5 \) is:
\[
\boxed{T = 151}
\]