# Algebra Puzzle – Challenge 34

Looking for a math puzzle to tease your brain and challenge your logic? If so, then look no further!

## 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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