Difference between revisions of "2013 AMC 8 Problems/Problem 4"

(help unicode inside of latex is not cool i think it's the mod)
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Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
 
Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?
  
<math>\textbf{(A)}\ &#036;120 \qquad \textbf{(B)}\ &#036;128 \qquad \textbf{(C)}\ &#036;140 \qquad \textbf{(D)}\ &#036;144 \qquad \textbf{(E)}\ &#036;160</math>
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<math>\textbf{(A)}\ </math>120 \qquad \textbf{(B)}\ <math>128 \qquad \textbf{(C)}\ </math>140 \qquad \textbf{(D)}\ <math>144 \qquad \textbf{(E)}\ </math>160<math>
  
 
==Solution==
 
==Solution==
Judi's seven friends each paid &#036;2.50 for her, so the total amount of money that was paid for her was <math>7\cdot &#036;2.50 = &#036;17.50</math>. This is Judi's portion of the bill; what she was supposed to pay.
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Judi's seven friends each paid &#036;2.50 for her, so the total amount of money that was paid for her was </math>7\cdot <math>2.50 = </math>17.50<math>. This is Judi's portion of the bill; what she was supposed to pay.
  
Judi was supposed to pay <math>\frac{1}{8}</math> of the total bill, so the total bill must be <math>8\cdot &#036;17.50 = \textbf{(C)}\ &#036;140</math>.
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Judi was supposed to pay </math>\frac{1}{8}<math> of the total bill, so the total bill must be </math>8\cdot <math>17.50 = \textbf{(C)}\ </math>140$.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2013|num-b=3|num-a=5}}
 
{{AMC8 box|year=2013|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 12:08, 27 November 2013

Problem

Eight friends ate at a restaurant and agreed to share the bill equally. Because Judi forgot her money, each of her seven friends paid an extra $2.50 to cover her portion of the total bill. What was the total bill?

$\textbf{(A)}$120 \qquad \textbf{(B)}\ $128 \qquad \textbf{(C)}$140 \qquad \textbf{(D)}\ $144 \qquad \textbf{(E)}$160$==Solution== Judi's seven friends each paid &#036;2.50 for her, so the total amount of money that was paid for her was$ (Error compiling LaTeX. Unknown error_msg)7\cdot $2.50 =$17.50$. This is Judi's portion of the bill; what she was supposed to pay.

Judi was supposed to pay$ (Error compiling LaTeX. Unknown error_msg)\frac{1}{8}$of the total bill, so the total bill must be$8\cdot $17.50 = \textbf{(C)}$140$.

See Also

2013 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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

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