Let the integers describing Mary and Frank be M and F respectively.
Mary has 28 dollars more than Frank.
M = F + 28
F = M - 28
Mary has given \(\frac{1}{4}\) of her money to frank.
The amount with Mary is now \(M - \frac{M}{4} = \frac{3M}{4}\)
The amount with Frank is now \(F + \frac{M}{4}\)
Now Frank has 50% of the money that Mary has.
50%(Mary) = Frank
\(\frac{50}{100}(\frac{3M}{4}) = F + \frac{M}{4}\)
\(\frac{1}{2}(\frac{3M}{4}) = F + \frac{M}{4}\)
\(\frac{3M}{8} = F + \frac{M}{4}\)
\(\frac{3M}{8} - \frac{M}{4} = F\)
\(\frac{M}{8} = F\)
\(\frac{M}{8} = M - 28\)
\(28 = M - \frac{M}{8}\)
\(28 = \frac{7M}{8}\)
\(M = \frac{28*8}{7}\)
M = 32Choice [C] is the answer.
IMO, for simple questions such as these, plugging in options one by one might take more time than actually solving the question. Though plugging in options might save the day in some scenarios, this is not one.
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