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

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==Problem==
 
==Problem==
  
Chandra pays an on-line service provider a fixed monthly fee plus an hourly charge for connect time. Her December bill was <math></math>12.48<math>, but in January her bill was </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?
  
<math>\textbf{(A)} </math>2.53 \qquad\textbf{(B)} <math>5.06 \qquad\textbf{(C)} </math>6.24 \qquad\textbf{(D)} <math>7.42 \qquad\textbf{(E)} </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==
  
Let </math>x<math> be the fixed fee, and </math>y<math> be the amount she pays for the minutes she used in the first month.
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Let <math>x</math> be the fixed fee, and <math>y</math> be the amount she pays for the minutes she used in the first month.
  
</math>x+y=12.48<math>
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<math>x+y=12.48</math>
  
</math>x+2y=17.54<math>
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<math>x+2y=17.54</math>
  
</math>y=5.06<math>
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<math>y=5.06</math>
  
</math>x=7.42<math>
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<math>x=7.42</math>
  
We want the fixed fee, which is </math>\boxed{\text{D}}$
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We want the fixed fee, which is <math>\boxed{\text{D}}</math>
  
 
==See Also==
 
==See Also==

Latest revision as of 09:49, 8 November 2021

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 $\boxed{\text{D}}$

See Also

2000 AMC 10 (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 AMC 10 Problems and Solutions

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