# Algebra Puzzle – Challenge 34

Are you seeking 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 ### The Absolute Best Book to Challenge Your Smart Student! Original price was:$16.99.Current price is: $11.99. Satisfied 123 Students 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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