Question

A college student takes the same number of credits each semester. Before beginning college, the student had some credits earned while in high school. After 3 semesters, the student had 41 credits, and after 6 semesters, the student had 68 credits. If C(t), is the number of credits after t semesters, write the equation that correctly models this situation.

Answer 1

C(t) = 9t + 14

Explanation:

write two equations with the given information

x + 6y = 68

x + 3y = 41

(x and y are just random variables, with x being the number of credits from high school and y being the number of credits earned each semester)

subtract (x+3y=41) from (x+6y=68) to get 3y=27

y = 9

then plug back in to one of the equations to find x

x + 3(9) = 41

x + 27 = 41

x = 14

then write the equation for C(t)

C(t) = 9t + 14

because you start with 14 credits from high school then add 9 credits for each semester taken