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>\</ | + | 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? |
| − | <math>\mathrm{(A)}\ \</ | + | <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< | + | 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>x+y=12.48<math> |
| − | <math>x+2y=17.54< | + | </math>x+2y=17.54<math> |
| − | <math>y=5.06< | + | </math>y=5.06<math> |
| − | <math>x=7.42< | + | </math>x=7.42<math> |
| − | We want the fixed fee, which is <math>\boxed{\text{D}} | + | We want the fixed fee, which is </math>\boxed{\text{D}}$ |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2000|num-b=3|num-a=5}} | {{AMC10 box|year=2000|num-b=3|num-a=5}} | ||
| + | [[Category:Introductory Algebra Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:19, 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
$
because she used twice as much connect time as in December. What is the fixed monthly fee?
2.53 \qquad\mathrm{(B)}\ $ 
6.24 \qquad\mathrm{(D)}\ $ 
8.77$==Solution==
Let$ (Error compiling LaTeX. Unknown error_msg)x
y
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
\boxed{\text{D}}$
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. 
