Algebra Puzzle – Challenge 34
This challenge is a work-rate problem: eight workers build a house in twenty days, and you are asked how many workers finish it in four. Because workers and days vary inversely, the total worker-days stays fixed at 160. A full worked solution follows the question.
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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