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>\$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>\ | + | <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 < | + | 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> |
| − | < | + | <math>x+2y=17.54</math> |
| − | < | + | <math>y=5.06</math> |
| − | < | + | <math>x=7.42</math> |
| − | We want the fixed fee, which is < | + | We want the fixed fee, which is <math>\boxed{\text{D}}</math>. |
| + | |||
| + | ==Video Solution by Daily Dose of Math== | ||
| + | |||
| + | https://youtu.be/9fpwHHTh23I?si=RZHpwnmRleepF_ld | ||
| + | |||
| + | ~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}} | ||
| − | |||
{{MAA Notice}} | {{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 
, but in January her bill was 
because she used twice as much connect time as in December. What is the fixed monthly fee?
Solution
Let 
be the fixed fee, and 
be the amount she pays for the minutes she used in the first month.
We want the fixed fee, which is 
.
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. 
