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>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? | + | 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>\mathrm{(A)}\ \$ 2.53 \qquad\mathrm{(B)}\ \$ 5.06 \qquad\mathrm{(C)}\ \$ 6.24 \qquad\mathrm{(D)}\ \$ 7.42 \qquad\mathrm{(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> |
==See Also== | ==See Also== | ||
Revision as of 07:52, 25 June 2021
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 
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. 
