Difference between revisions of "1999 AMC 8 Problems/Problem 7"

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==problem==
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==Problem==
  
The third exit on a highway is located at milepost 40 and the tenth exit is at
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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?
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?
 
(A) 90 (B) 100 (C) 110 (D) 120 (E) 130
 
  
==solution==
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<math>\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 110 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 130</math>
  
(E) 130:  There are 160-40=120 miles between the third and tenth exits, so the service
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==Solution==
center is at milepost 40+ (3/4) 120= 40+90=130.
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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>.
  
 
==See Also==
 
==See Also==
  
 
{{AMC8 box|year=1999|num-b=6|num-a=8}}
 
{{AMC8 box|year=1999|num-b=6|num-a=8}}
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{{MAA Notice}}

Revision as of 14:07, 21 October 2016

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?

$\text{(A)}\ 90 \qquad \text{(B)}\ 100 \qquad \text{(C)}\ 110 \qquad \text{(D)}\ 120 \qquad \text{(E)}\ 130$

Solution

There are $160-40=120$ miles between the third and tenth exits, so the service center is at milepost $40+(3/4)(120) = 40+90=\boxed{\text{(E)}\ 130}$.

See Also

1999 AMC 8 (ProblemsAnswer KeyResources)
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

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