Beshmi invested $\frac{1}{5}$ of her savings in Company $\mathrm{X}, 42 \%$ in Company Y, and the remainder in Company Z. If Beshmi invested $\$ 10500$ in Company Y, how much did she invest in Company Z?
(A) $\$ 25000$
(B) $\$ 15500$
(C) $\$ 14000$
(D) $\$ 9500$
(E) $\$ 5000$
Solution 1

Since $\frac{1}{5}$ is equivalent to $20 \%$, then Beshmi invests a total of $20 \%+42 \%=62 \%$ of her savings in Companies X and Y, leaving $100 \%-62 \%=38 \%$ for Company Z.

Since $42 \%$ of her savings is $\$ 10500$, then $38 \%$ should be just slightly less than this amount, so of the given choices, must be $\$ 9500$.

## Solution 2

Since $\frac{1}{5}$ is equivalent to $20 \%$, then Beshmi invests a total of $20 \%+42 \%=62 \%$ of her savings in Companies X and Y, leaving $100 \%-62 \%=38 \%$ for Company Z.

Since $42 \%$ of her savings is $\$ 10500$, then $1 \%$ of her savings is $\$ 10000 \div 42=\$ 250$.

But $38 \%=38 \times 1 \%$, which is $38 \times \$ 250=\$ 9500$ here.

Therefore, she invests $\$ 9500$ in Company Z.

ANSWER: (D)