Last month Maria hiked a total of 90 miles on two hiking trails: a 5-mile mountain trail and a 10-mile canal trail. Let x represent the number of times Maria hiked the mountain trail, and let y represent the number of times Maria hiked the canal trail.
Which equation can be used to find the number of times Maria hiked each trail?
A. 50 - 10y = 5x
B. 5x - 10y = 90
C. x + y = 90
D. 90 + 10y = 5x
Answer (2)
Take all the possible triangles. That is, all triplets of numbers a,b,c that have a total sum of 2014 and obey the conditions: a<b+c;b<c+a;c<a+b. All triangles have been taken 3 times, so divide the count by 3.
To find non-congruent triangles with integer side lengths and a perimeter of 2014, we use triangle inequalities which determine the range of possible side lengths. The side lengths must satisfy a + b > 1007 and the maximum side length c must be less than or equal to 671. Calculating across the valid values of side lengths yields a total of 168 valid triangles.
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