Question

the cost of tuition at a certain college varies directly as the number of credit hours taken. for the academic year 2005 - 2006, the cost of 12 credit hours was $1154. what did 11 credit hours cost? the cost of 11 credit hours was $

Explanation:

Step1: Define direct variation formula

Let \( C \) be the cost of tuition and \( h \) be the number of credit hours. Since they vary directly, \( C = kh \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that when \( h = 12 \), \( C = 1154 \). Substitute into the formula: \( 1154 = k \times 12 \). Solve for \( k \): \( k=\frac{1154}{12}=\frac{577}{6}\approx96.17 \)

Step3: Calculate cost for 11 credit hours

Now, use \( h = 11 \) and \( k=\frac{577}{6} \) in \( C = kh \). So \( C=\frac{577}{6}\times11=\frac{6347}{6}\approx1057.83 \)

Answer:

\( 1057.83 \) (or \(\frac{6347}{6}\) if exact fraction is preferred)