Difference between revisions of "1985 AJHSME Problems/Problem 14"
(New page: ==Solution== The most straightforward method would be to calculate both prices, and subtract. But there's a better method... Before we start, it's always good to convert the word problem...) |
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+ | ==Problem== | ||
+ | |||
+ | The difference between a <math>6.5\% </math> sales tax and a <math>6\% </math> sales tax on an item priced at <dollar/><math>20</math> before tax is | ||
+ | |||
+ | <math>\text{(A)}</math> <dollar/><math>.01</math> | ||
+ | |||
+ | <math>\text{(B)}</math> <dollar/><math>.10</math> | ||
+ | |||
+ | <math>\text{(C)}</math> <dollar/><math>.50</math> | ||
+ | |||
+ | <math>\text{(D)}</math> <dollar/><math>1</math> | ||
+ | |||
+ | <math>\text{(E)}</math> <dollar/><math>10</math> | ||
+ | |||
==Solution== | ==Solution== | ||
The most straightforward method would be to calculate both prices, and subtract. But there's a better method... | The most straightforward method would be to calculate both prices, and subtract. But there's a better method... | ||
− | Before we start, it's always good to convert the word problems into | + | Before we start, it's always good to convert the word problems into expressions, we can solve. |
+ | |||
+ | So we know that the price of the object after a <math>6.5\% </math> increase will be <math>20 \times 6.5\% </math>, and the price of it after a <math>6\% </math> increase will be <math>20 \times 6\% </math>. And what we're trying to find is <math>6.5\% \times 20 - 6\% \times 20</math>, and if you have at least a little experience in the field of algebra, you'll notice that both of the items have a common factor, <math>20</math>, and we can factor the expression into | ||
+ | <cmath>\begin{align*} | ||
+ | (6.5\% - 6\% ) \times 20 &= (.5\% )\times 20 \ | ||
+ | &= \frac{.5}{100}\times 20 \ | ||
+ | &= \frac{1}{200}\times 20 \ | ||
+ | &= .10 \ | ||
+ | \end{align*}</cmath> | ||
− | + | <math>.10</math> is choice <math>\boxed{\text{B}}</math> | |
− | + | ==See Also== | |
− | + | [[1985 AJHSME Problems]] |
Revision as of 17:45, 13 January 2009
Problem
The difference between a sales tax and a sales tax on an item priced at <dollar/> before tax is
<dollar/>
<dollar/>
<dollar/>
<dollar/>
<dollar/>
Solution
The most straightforward method would be to calculate both prices, and subtract. But there's a better method...
Before we start, it's always good to convert the word problems into expressions, we can solve.
So we know that the price of the object after a increase will be , and the price of it after a increase will be . And what we're trying to find is , and if you have at least a little experience in the field of algebra, you'll notice that both of the items have a common factor, , and we can factor the expression into
is choice