Jeff says, If Kevin gives me $30, he will have half as much as Daniel. But, if Daniel gives me $30 then three of us will have the same amount. What is the total amount of money that Jeff, Kevin, and Daniel have among themselves?


Answer:

$270

Step by Step Explanation:
  1. Let us first look at the second statement,
    'If Daniel gives Jeff $30 then three of us will have the same amount.'
    This means that if Kevin had x amount,
    Jeff had $(x - 30) and
    Daniel had $(x + 30).
  2. Now, look at the first statement,
    'If Kevin gives Jeff 30, Kevin will have half as much as Daniel.'
    That is,
    x - 30 = 1/2 (x + 30)
  3. Let us solve the above equation,
      x - 30 = 1/2 (x + 30)
    ⇒ 2x - 2(30) = x + 30
    ⇒ 2x -x = 2(30) + 30
    ⇒ x = 3(30)
    ⇒ x = 90
  4. Now, the total amount Jeff, Kevin, and Daniel have:
    = (x - 30) + x + (x + 30)
    = 3x
    = 3 × 90
    = $270

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