In captivity, the average life span of an elephant is 25 years more than that of an elk. The sum of the two ages is 55 years. What is the average life span of an elk in captivity?
Answer (2)
The average life span of an elk in captivity is 15 years, derived by setting up equations based on the relationship between its age and that of an elephant, whose life span is 25 years more. By solving these equations, we find that the elk's life span is 15 years. Thus, both the relationship and the total age provided in the problem help us find the answer systematically.
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Define variables: Let e be the average life span of an elephant and k be the average life span of an elk.
Write equations: e = k + 25 and e + k = 55 .
Substitute the first equation into the second: ( k + 25 ) + k = 55 .
Solve for k : k = 15 . The average life span of an elk in captivity is 15 years.
Explanation
Problem Analysis Let's analyze the problem. We are given two pieces of information: the relationship between the life spans of elephants and elks, and the sum of their life spans. We need to find the life span of the elk.
Define Variables Let's define our variables:
Let e be the average life span of an elephant. Let k be the average life span of an elk.
Write Equations From the problem, we can write two equations:
e = k + 25 (The average life span of an elephant is 25 years more than that of an elk) e + k = 55 (The sum of the two ages is 55 years)
Substitution Now we can substitute the first equation into the second equation to solve for k :
( k + 25 ) + k = 55
Combine Like Terms Combine like terms:
2 k + 25 = 55
Isolate the Variable Subtract 25 from both sides:
2 k = 55 − 25 2 k = 30
Solve for k Divide both sides by 2:
k = 2 30 k = 15
Final Answer So, the average life span of an elk in captivity is 15 years.
Examples
Understanding the life spans of animals can help in conservation efforts. For example, knowing the average life span of an elk and an elephant in captivity can help zoos and wildlife parks plan for their long-term care and resource allocation. This type of problem, involving setting up equations based on given information, is also useful in many real-world scenarios such as budgeting, project management, and resource allocation, where you need to determine unknown quantities based on known relationships and constraints.
