New Zealand
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
- 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). - 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) - 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 - Now, the total amount Jeff, Kevin, and Daniel have:
= (x - 30) + x + (x + 30)
= 3x
= 3 × 90
= $270
