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>\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==

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. Unknown error_msg)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$$ (Error compiling LaTeX. Unknown error_msg)x+2y=17.54$$ (Error compiling LaTeX. Unknown error_msg)y=5.06$$ (Error compiling LaTeX. Unknown error_msg)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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