1998 AJHSME Problems/Problem 9

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Problem 9

For a sale, a store owner reduces the price of a <dollar/>10 scarf by $20\%$. Later the price is lowered again, this time by one-half the reduced price. The price is now

$\text{(A)}\ 2.00\text{ dollars} \qquad \text{(B)}\ 3.75\text{ dollars} \qquad \text{(C)}\ 4.00\text{ dollars} \qquad \text{(D)}\ 4.90\text{ dollars} \qquad \text{(E)}\ 6.40\text{ dollars}$

Solution 1

$100\%-20\%=80\%$

$10\times80\%=$10\times0.8$$ (Error compiling LaTeX. Unknown error_msg)10\times0.8=8$$ (Error compiling LaTeX. Unknown error_msg)\frac{8}{2}=4=\boxed{C}$==Solution 2==

The first discount has percentage 20, which is then discounted again for half of the already discounted price.$ (Error compiling LaTeX. Unknown error_msg)100-20=80$$ (Error compiling LaTeX. Unknown error_msg)\frac{80}{2}=40$$ (Error compiling LaTeX. Unknown error_msg)40\%\times10=10\times0.4=4=\boxed{C}$


See also

1998 AJHSME (ProblemsAnswer KeyResources)
Preceded by
1997 AJHSME
Followed by
1999 AMC 8
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All AJHSME/AMC 8 Problems and Solutions