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GRE 9- Peter's bank account has p dollars. John's bank account has 5 times what Peter's bank account....

By spartan
Peter's bank account has p dollars. John's bank account has 5 times what Peter's bank account has and 1/3 what Fred's bank account has. How much more is in Fred's bank account than is in Peter's bank account, in terms of p? A) 15p B) 14p C) 4p D) (2/3)p E) (1/3)p

  1. Assign letters to each man's bank account:
    Peter = p.
    John = j.
    Fred = f.
  2. Now translate the sentences from the question into equations:
    j = 5p "John's bank account has 5 times what Peter's bank account has"
    j = (1/3)f "John's bank account has ... 1/3 what Fred's bank account has"
  3. Combine the two equations to yield:
    5p = j = (1/3)f
    5p = (1/3)f.
  4. Divide both sides by 1/3 (the same as multiplying by 3) to yield:
    15p = f
    Translated back into words, this means Fred has 15p dollars in his account.
  5. We are interested in the difference between the amount Fred has (15p) and the amount Peter has (p). Subtract p from 15p to yield 14p.
    Fred - Peter =
    15p - p = 14p
    Thus, B is correct.

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