Algebra Puzzle – Challenge 58

Challenge:

Three times of Michael’s money equals \(\frac{2}{3}\) of Jackson’s money. If the sum of their money is $2200, how much money does Michael have?

A- 200

B- 400

C- 1000

D- 1600

E- 1800

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Let M be Michael’s money and J be Jackson’s money. Therefore:
M + J = 2200 and 3M \(= \frac{2}{3} J →M = \frac{2}{9} J\)
Replace the value of M in the first equation with its value in the second equation.
\(\frac{2}{9} J + J = 2200→ J = 1800\)
\(M = \frac{2}{9} J → M = \frac{2}{9} (1800) = 400\)
Michael has $400.

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