Algebra Puzzle – Challenge 34

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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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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