Difference between revisions of "2007 AMC 12A Problems/Problem 1"

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One ticket to a show costs $20 at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickers using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?
 
One ticket to a show costs $20 at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickers using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?
  
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<math>\mathrm{(A)}\ 2\qquad \mathrm{(B)}\ 5\qquad \mathrm{(C)}\ 10\qquad \mathrm{(D)}\ 15\qquad \mathrm{(E)}\ 20</math>
  
 
== Solution ==
 
== Solution ==
P=the amount Pam spent
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$P$ = the amount Pam spent
S=the amount Susan spent
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$S$ = the amount Susan spent
  
* <math>P=5*(20*.7)=70</math>
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* <math>\displaystyle P=5 \displaystyle  \cdot (20 \cdot .7) = 70</math>
* <math>S=4*(20*.75)=60</math>
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* <math>\displaystyle S=4 \cdot (20 \cdot .75) = 60</math>
  
 
Pam pays 10 more dollars than Susan.
 
Pam pays 10 more dollars than Susan.
  
 
== See also ==
 
== See also ==
* [[2007 AMC 12A Problems/Problem 2 | Next problem]]
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{{AMC12 box|year=2007|ab=A|before=First question|num-a=2}}
* [[2007 AMC 12A Problems]]
 

Revision as of 10:37, 9 September 2007

Problem

One ticket to a show costs $20 at full price. Susan buys 4 tickets using a coupon that gives her a 25% discount. Pam buys 5 tickers using a coupon that gives her a 30% discount. How many more dollars does Pam pay than Susan?

$\mathrm{(A)}\ 2\qquad \mathrm{(B)}\ 5\qquad \mathrm{(C)}\ 10\qquad \mathrm{(D)}\ 15\qquad \mathrm{(E)}\ 20$

Solution

$P$ = the amount Pam spent $S$ = the amount Susan spent

  • $\displaystyle P=5 \displaystyle  \cdot (20 \cdot .7) = 70$
  • $\displaystyle S=4 \cdot (20 \cdot .75) = 60$

Pam pays 10 more dollars than Susan.

See also

2007 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
First question
Followed by
Problem 2
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All AMC 12 Problems and Solutions