MATH SOLVE

5 months ago

Q:
# See attached photo belowThe last part was cut off but I am writing it in here:Which library charges more for each book loaned?A.) The first libraryB.) The second libraryC.) They both Charge the same for each book loaned.Which library has a Cheaper subscription fee?A.) The first libraryB.) The second libraryC.) They both have the same subscription fee

Accepted Solution

A:

Answer:Library 2 charges more for each book loaned.Library 1 has a cheaper subscription fee.Step-by-step explanation:Based on the table, we can write the equation for the cost of borrowing from Library 2 using the two-point form of the equation of a line: y = (y2 -y1)/(x2 -x1)(x -x1) +y1for (x1, y1) = (2, 15.50) and (x2, y2) = (8, 26) this equation becomes ... y = (26 -15.50)/(8 -2)(x -2) +15.50 . . . . . fill in the values y = (10.50/6)(x -2) +15.50 . . . . . . . . . . . . simplify a bit y = 1.75x -3.50 +15.50 . . . . . . simplify moreIn the above, we have x = number of books; y = cost. We can use "n" and "C" for those, respectively, as in the equation for Library 1. Then the monthly cost for Library 2 is ... C = 12 + 1.75n . . . . . . . arranged to the same form as for Library 1_____Now, we can answer the questions.Library 2 charges more for each book loaned. (1.75 vs 1.50 for Library 1)Library 1 has a cheaper subscription fee. (10 vs 12 for Library 2)_____The numbers in the cost equations are ... C = (subscription fee) + (cost per book loaned)·n