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Difference between revisions of "1986 AJHSME Problems/Problem 15"

(→‎Solution)
Line 16: Line 16:
  
 
First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week.
 
First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week.
 +
<cmath>\begin{align*}
 +
180 \times 50\% &= 180 \times \frac{1}{2} \\
 +
&= 90 \\
 +
\end{align*}</cmath>
  
−
<math>180 \times 50\% = 180 \times \frac{1}{2} = 90</math>
+
If we discount <math>20\% </math>, then <math>80 \% </math> will be left, so after the second discount, we get
 +
<cmath>\begin{align*}
 +
90 \times 80\% &= 90 \times \frac{8}{10} \\
 +
&= 9 \times 8 \\
 +
&= 72 \\
 +
\end{align*}</cmath>
  
−
Then we factor in the <math>20\%</math> discount.
+
<math>\boxed{\text{B}}</math>
−
 
 
−
<math>90 \times 20\% = 90 \times \frac{2}{10} = 9 \times 2 = 18</math>
 
−
 
 
−
Thus it would cost <math> \</math>18 dollars!
 
  
 
==See Also==
 
==See Also==
  
 
[[1986 AJHSME Problems]]
 
[[1986 AJHSME Problems]]

Revision as of 18:27, 24 January 2009

Problem

Sale prices at the Ajax Outlet Store are $50\%$ below original prices. On Saturdays an additional discount of $20\%$ off the sale price is given. What is the Saturday price of a coat whose original price is <dollar/>$180$?

$\text{(A)}$ <dollar/>$54$

$\text{(B)}$ <dollar/>$72$

$\text{(C)}$ <dollar/>$90$

$\text{(D)}$ <dollar/>$108$

$\text{(D)}$ <dollar/>$110$

Solution

First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week. \begin{align*} 180 \times 50\% &= 180 \times \frac{1}{2} \\ &= 90 \\ \end{align*}

If we discount $20\%$, then $80 \%$ will be left, so after the second discount, we get \begin{align*} 90 \times 80\% &= 90 \times \frac{8}{10} \\ &= 9 \times 8 \\ &= 72 \\ \end{align*}

$\boxed{\text{B}}$

See Also

1986 AJHSME Problems

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