2017 AMC 12B Problem 1

Question

Kymbrea’s comic book collection currently has

30

comic books in it, and she is adding to her collection at the rate of

2

comic books per month. LaShawn’s collection currently has

10

comic books in it, and he is adding to his collection at the rate of

6

comic books per month. After how many months will LaShawn’s collection have twice as many comic books as Kymbrea’s?

1

4

5

20

25

After

m

months the collections hold

30 + 2m

and

10 + 6m

comic books

Set

10 + 6m = 2(30 + 2m)

and solve for

m

After

m

months, Kymbrea has

30 + 2m

comic books and LaShawn has

10 + 6m.

Setting

10 + 6m = 2(30 + 2m)

gives

10 + 6m = 60 + 4m,

so

2m = 50

and

m = 25.

Thus, the correct answer is E.

Problem 1 in other years