2008 iTest Problems/Problem 17
Problem
One day when Wendy is riding her horse Vanessa, they get to a field where some tourists are following Martin (the tour guide) on some horses. Martin and some of the workers at the stables are each leading extra horses, so there are more horses than people. Martin's dog Berry runs around near the trail as well. Wendy counts a total of heads belonging to the people, horses, and dog. She counts a total of
legs belonging to everyone, and notes that nobody is missing any legs.
Upon returning home Wendy gives Alexis a little problem solving practice, "I saw heads and
legs belonging to people, horses, and dogs. Assuming two legs per person and four for the other animals, how many people did I see?" Alexis scribbles out some algebra and answers correctly. What is her answer?
Solution
Let be the number of humans,
be the number of horses, and
be the number of dogs. Write a system of equations (and one inequality).
Multiply the first equation by
to get
Subtract the second equation to get
When the value is plugged in, we can find multiple integers
and
that satisfy the equations and inequality. Thus, there are
people.
See Also
2008 iTest (Problems) | ||
Preceded by: Problem 16 |
Followed by: Problem 18 | |
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