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Difference between revisions of "2000 AMC 10 Problems/Problem 4"

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==Problem==
 
==Problem==
  
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Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was <math>\</math><math>12.48</math>, but in January her bill was <math>\</math><math>17.54</math> because she used twice as much connect time as in December. What is the fixed monthly fee?
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Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was <math>\$12.48</math>, but in January her bill was <math>\$17.54</math> because she used twice as much connect time as in December. What is the fixed monthly fee?
  
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<math>\mathrm{(A)}\ \</math> <math>2.53 \qquad\mathrm{(B)}\ \</math> <math>5.06 \qquad\mathrm{(C)}\ \</math> <math>6.24 \qquad\mathrm{(D)}\ \</math> <math>7.42 \qquad\mathrm{(E)}\ \</math> <math>8.77</math>
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<math>\textbf{(A)}\ \$ 2.53 \qquad\textbf{(B)}\ \$ 5.06 \qquad\textbf{(C)}\ \$ 6.24 \qquad\textbf{(D)}\ \$ 7.42 \qquad\textbf{(E)}\ \$ 8.77</math>
  
 
==Solution==
 
==Solution==
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<math>x=7.42</math>
 
<math>x=7.42</math>
  
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We want the fixed fee, which is <math>\boxed{\text{D}}</math>
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We want the fixed fee, which is <math>\boxed{\text{D}}</math>.
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 +
==Video Solution by Daily Dose of Math==
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https://youtu.be/9fpwHHTh23I?si=RZHpwnmRleepF_ld
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~Thesmartgreekmathdude
  
 
==See Also==
 
==See Also==
  
 
{{AMC10 box|year=2000|num-b=3|num-a=5}}
 
{{AMC10 box|year=2000|num-b=3|num-a=5}}
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{{MAA Notice}}

Latest revision as of 23:37, 14 July 2024

Problem

Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was $$12.48$, but in January her bill was $$17.54$ because she used twice as much connect time as in December. What is the fixed monthly fee?

$\textbf{(A)}\ $ 2.53 \qquad\textbf{(B)}\ $ 5.06 \qquad\textbf{(C)}\ $ 6.24 \qquad\textbf{(D)}\ $ 7.42 \qquad\textbf{(E)}\ $ 8.77$

Solution

Let $x$ be the fixed fee, and $y$ be the amount she pays for the minutes she used in the first month.

$x+y=12.48$

$x+2y=17.54$

$y=5.06$

$x=7.42$

We want the fixed fee, which is $\boxed{\text{D}}$.

Video Solution by Daily Dose of Math

https://youtu.be/9fpwHHTh23I?si=RZHpwnmRleepF_ld

~Thesmartgreekmathdude

See Also

2000 AMC 10 (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 AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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