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Difference between revisions of "1986 AJHSME Problems/Problem 15"
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==Problem==
 
==Problem==
  
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Sale prices at the Ajax Outlet Store are <math>50\% </math> below original prices.  On Saturdays an additional discount of <math>20\% </math> off the sale price is given.  What is the Saturday price of a coat whose original price is <dollar/><math>180</math>?
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Sale prices at the Ajax Outlet Store are <math>50\% </math> below original prices.  On Saturdays an additional discount of <math>20\% </math> off the sale price is given.  What is the Saturday price of a coat whose original price is <math>\textdollar 180</math>?
  
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<math>\text{(A)}</math> <dollar/><math>54</math>
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<math>\text{(A)}\ \$54 \qquad \text{(B)}\ \$72 \qquad \text{(C)}\ \$90 \qquad \text{(D)}\ \$108 \qquad \text{(E)}\ \$110</math>
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<math>\text{(B)}</math> <dollar/><math>72</math>
 
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<math>\text{(C)}</math> <dollar/><math>90</math>
 
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<math>\text{(D)}</math> <dollar/><math>108</math>
 
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<math>\text{(D)}</math> <dollar/><math>110</math>
 
  
 
==Solution==
 
==Solution==
  
 
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*}
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180 \times 50\% &= 180 \times \frac{1}{2} \\
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&= 90 \\
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\end{align*}</cmath>
  
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<math>180 \times 50\% = 180 \times \frac{1}{2} = 90</math>
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If we discount <math>20\% </math>, then <math>80 \% </math> will be left, so after the second discount, we get
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<cmath>\begin{align*}
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Then we factor in the <math>20\%</math> discount.
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90 \times 80\% &= 90 \times \frac{8}{10} \\
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&= 9 \times 8 \\
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<math>90 \times 20\% = 90 \times \frac{2}{10} = 9 \times 2 = 18</math>
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&= 72 \\
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\end{align*}</cmath>
  
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Thus it would cost <math> \</math>18$ dollars!
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<math>\boxed{\text{B}}</math>
  
 
==See Also==
 
==See Also==
  
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[[1986 AJHSME Problems]]
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{{AJHSME box|year=1986|num-b=14|num-a=16}}
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[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 12:02, 18 June 2025

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 $\textdollar 180$?

$\text{(A)}\ $54 \qquad \text{(B)}\ $72 \qquad \text{(C)}\ $90 \qquad \text{(D)}\ $108 \qquad \text{(E)}\ $110$

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 • Answer Key • Resources)
Preceded by
Problem 14 		Followed by
Problem 16
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. AMC Logo.png

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