IMAT 2012 Q17 [DVDs]

Three months ago, Jane had 5 times as many DVDs as Duncan. Since then they have both bought 12 more DVDs. Jane now has twice as many as Duncan.

How many DVDs does Jane have now?

A. 72
B. 32
C. 52
D. 62
E. 42

Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
    Eliminate any non-essential information
  • Draw a picture, graph, or equation
    In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.
  1. Define your variable. Let “ j ” stand for Jane and let “ d ” stand for Ducan.

  2. Set up a relationship for the variables 3 months ago.

j = 5d

  1. Set up a current relationship. We know that they both have an increase of 12 DVDs, and we also know that j currently has 2 times more DVDs than Duncan after they both had the increase of 12

j+12=2(d+12)

  1. Sub in the first equation into the second and solve.

5d+12 = 2(d+12)

5d+12 = 2d+24

3d = 12

d=4

Now solve for j
j=5d

j=5(4)

j=20

j now has 20+12 = 32 DVDs.

\fcolorbox{red}{grey!30}{Therefore B is the answer.}

For more practice with this style of problem, try IMAT 2011 Q34