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 $1164. what did 11 credit hours cost? the cost of 11 credit hours was $

Explanation:

Step1: Find the cost per credit hour

Let \( C \) be the cost and \( h \) be the number of credit hours. Since \( C \) varies directly as \( h \), we have \( C = kh \) (where \( k \) is the constant of proportionality). We know that when \( h = 12 \), \( C = 1164 \). So we can find \( k \) by substituting these values into the equation: \( 1164 = k \times 12 \). Solving for \( k \), we divide both sides by 12: \( k=\frac{1164}{12}=97 \).

Step2: Calculate the cost for 11 credit hours

Now that we know \( k = 97 \), we can find the cost for 11 credit hours. Using the direct variation formula \( C = kh \), we substitute \( k = 97 \) and \( h = 11 \): \( C = 97\times11 = 1067 \).

Answer:

1067