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><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?
  
<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>\mathrm{(A)}\ \$ </math>2.53 \qquad\mathrm{(B)}\ \$ <math>5.06 \qquad\mathrm{(C)}\ \$ </math>6.24 \qquad\mathrm{(D)}\ \$ <math>7.42 \qquad\mathrm{(E)}\ \$ </math>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}}</math>
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We want the fixed fee, which is </math>\boxed{\text{D}}$
  
 
==See Also==
 
==See Also==

Latest revision as of 18:25, 19 April 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?

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

Let$ (Error compiling LaTeX. ! Missing $ inserted.)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$$ (Error compiling LaTeX. ! Missing $ inserted.)x+2y=17.54$$ (Error compiling LaTeX. ! Missing $ inserted.)y=5.06$$ (Error compiling LaTeX. ! Missing $ inserted.)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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