Algebra Puzzle – Challenge 34
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Challenge:
$464 is divided among Janet, Elliot, and Sarah. Janet received \(\frac{2}{3}\) of Elliot’s money and Sara received \(\frac{2}{5}\) of Janet’s money. How much money did Janet get?
A- 64
B- 100
C- 160
D- 240
E- 280
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The correct answer is C.
Let J be Janet’s money, E be Elliot’s money, and S be Sarah’s money. Therefore,
\(J + E + S = 464\)
\(J = \frac{2}{3} E → E = \frac{3}{2} J\) and \(S = \frac{2}{5} J\)
Replace the value of E and S in the first equation with their values in the second and third equations:
\(J + \frac{3}{2} J + \frac{2}{5} J = 464 → 1 \frac{19}{10} J = 464 → J = 160\)
Janet received $160!
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