dean and tara are photographers they take pictures of senior

dean and tara are photographers. they take pictures of seniors for high school yearbooks. they charge a standard fee for taking the pictures. theres also a charge for each set of prints ordered. so the number of sets of prints determines the total cost. let s stand for the sets of prints ordered write the rule that describes a students total cost.

SETS OF PRINTS (S) TOTAL COSTS

0 15

1 19

2 23

3 27

Solution

Since the number of sets of prints determines the total cost, there is a direct relationship between f (s), the total cost and the number of prints ordered (s). Let f (s) = as + b . When s = 0, f (s) = 15. Therefore, 15 = a*0 + b = b or, b = 15. Then we have f ( s ) = as + 15. Now, when s = 1, f(s) = 19. Therefore, 19 = a*1 + 15 or, a = 19 -15 = 4. Thus, f ( s ) = 4s + 15 . We can verify by substituting s = 2 and s = 3. When s = 2, f ( s ) = 4 * 2 + 15 = 8 + 15 = 23, and when s = 3, f ( s ) = 4*3 + 15 = 12 + 15 = 27. Thus, f (s) = 4s + 15 stands verified for all the sets of data given. Thus the rule that describes a student\'s total cost f ( s ) is f (s) = 4s + 15