1950 AHSME Problems/Problem 22
Problem
Successive discounts of and are equivalent to a single discount of:
Solution 1 (Kind of Lame)
Without loss of generality, assume something costs dollars. Then with each successive discount, it would cost dollars, then dollars. This amounts to a total of dollars off, so the single discount would be
Solution 2 (Technical)
Let the object cost dollars. After the $10%$ (Error compiling LaTeX. Unknown error_msg) discount, it's worth $(1-10%)x=0.9x$ (Error compiling LaTeX. Unknown error_msg) dollars. After a $20%$ (Error compiling LaTeX. Unknown error_msg) discount on that, it's worth $(1-20%)(0.9x)=0.72x$ (Error compiling LaTeX. Unknown error_msg). Say the single discount is of . Then . So , or $k=28%$ (Error compiling LaTeX. Unknown error_msg). So select .
~hastapasta
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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