Difference between revisions of "1999 AMC 8 Problems/Problem 7"
(Created page with "The distance between the two exits is 160-40=120. 120*(3/4)=90, so the exit is 90 miles away from the third exit or at the 40+90=130 milepost, so the answer is E.") |
Monkey land (talk | contribs) (→Video Solution) |
||
| (11 intermediate revisions by 7 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The | + | ==Problem== |
| + | |||
| + | The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center? | ||
| + | |||
| + | |||
| + | |||
| + | <math>\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 110 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 130</math> | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | There are <math>160-40=120</math> miles between the third and tenth exits, so the service center is at milepost <math>40+(3/4)(120) = 40+90=\boxed{\text{(E)}\ 130}</math>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | |||
| + | https://youtu.be/TFVzjTKrC5w Soo, DRMS, NM | ||
| + | |||
| + | ==Video Solution 2== | ||
| + | https://www.youtube.com/watch?v=qiumqqi4l9c | ||
| + | By YippieMath | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{AMC8 box|year=1999|num-b=6|num-a=8}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 20:27, 25 May 2025
Problem
The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center?
Solution
There are 
miles between the third and tenth exits, so the service center is at milepost 
.
Video Solution
https://youtu.be/TFVzjTKrC5w Soo, DRMS, NM
Video Solution 2
https://www.youtube.com/watch?v=qiumqqi4l9c By YippieMath
See Also
| 1999 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
