Difference between revisions of "2013 AMC 8 Problems/Problem 4"
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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)}\ | + | <math>\textbf{(A)}\ $120 \qquad \textbf{(B)}\ $128 \qquad \textbf{(C)}\ $140 \qquad \textbf{(D)}\ $144 \qquad \textbf{(E)}\ $160</math> |
==Solution== | ==Solution== | ||
| − | Judi's seven friends each paid $2.50 for her, so the total amount of money that was paid for her was < | + | Judi's seven friends each paid $2.50 for her, so the total amount of money that was paid for her was <math>7\cdot $2.50 = $17.50</math>. This is Judi's portion of the bill; what she was supposed to pay. |
| − | Judi 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 $17.50 = \textbf{(C)}\ $140</math>. |
==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 11:08, 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)}\ $160$ (Error compiling LaTeX. Unknown error_msg)
Solution
Judi's seven friends each paid $2.50 for her, so the total amount of money that was paid for her was 
. This is Judi's portion of the bill; what she was supposed to pay.
Judi was supposed to pay 
of the total bill, so the total bill must be 
.
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
