Answer :
Sure, let's solve the problem step-by-step:
1. Identify the Initial Weights and Rate of Change:
- The mountain gorilla initially weighs 135 pounds and gains 0.5 pounds per week.
- The Eastern gorilla initially weighs 141 pounds and loses 0.25 pounds per week.
2. Set Up an Equation to Represent Each Gorilla's Weight Over Time:
- For the mountain gorilla: Its weight over time can be represented as [tex]\(135 + 0.5w\)[/tex], where [tex]\(w\)[/tex] is the number of weeks.
- For the Eastern gorilla: Its weight over time can be represented as [tex]\(141 - 0.25w\)[/tex].
3. Determine When Their Weights are Equal:
- We need to find the number of weeks [tex]\(w\)[/tex] when both gorillas weigh the same. This means we set their weight expressions equal to each other:
[tex]\[
135 + 0.5w = 141 - 0.25w
\][/tex]
4. Formulate the Equation:
- Looking at the options provided:
A. [tex]\(135 + 0.5w = 141 + 0.25w\)[/tex] (Incorrect, because the Eastern gorilla is losing weight, not gaining.)
B. [tex]\(135 + 0.5w = 141 - 0.25w\)[/tex] (Correct, matches the situation described.)
C. [tex]\(135w + 0.5 = 141w + 0.25\)[/tex] (Incorrect form of the equation.)
D. [tex]\(135 - 0.5w = 141 + 0.25w\)[/tex] (Incorrect, as it does not represent the description given.)
5. Correct Equation:
- The correct equation to use is option B: [tex]\(135 + 0.5w = 141 - 0.25w\)[/tex].
This equation can be used to solve for [tex]\(w\)[/tex], which represents the number of weeks until the gorillas weigh the same amount.
1. Identify the Initial Weights and Rate of Change:
- The mountain gorilla initially weighs 135 pounds and gains 0.5 pounds per week.
- The Eastern gorilla initially weighs 141 pounds and loses 0.25 pounds per week.
2. Set Up an Equation to Represent Each Gorilla's Weight Over Time:
- For the mountain gorilla: Its weight over time can be represented as [tex]\(135 + 0.5w\)[/tex], where [tex]\(w\)[/tex] is the number of weeks.
- For the Eastern gorilla: Its weight over time can be represented as [tex]\(141 - 0.25w\)[/tex].
3. Determine When Their Weights are Equal:
- We need to find the number of weeks [tex]\(w\)[/tex] when both gorillas weigh the same. This means we set their weight expressions equal to each other:
[tex]\[
135 + 0.5w = 141 - 0.25w
\][/tex]
4. Formulate the Equation:
- Looking at the options provided:
A. [tex]\(135 + 0.5w = 141 + 0.25w\)[/tex] (Incorrect, because the Eastern gorilla is losing weight, not gaining.)
B. [tex]\(135 + 0.5w = 141 - 0.25w\)[/tex] (Correct, matches the situation described.)
C. [tex]\(135w + 0.5 = 141w + 0.25\)[/tex] (Incorrect form of the equation.)
D. [tex]\(135 - 0.5w = 141 + 0.25w\)[/tex] (Incorrect, as it does not represent the description given.)
5. Correct Equation:
- The correct equation to use is option B: [tex]\(135 + 0.5w = 141 - 0.25w\)[/tex].
This equation can be used to solve for [tex]\(w\)[/tex], which represents the number of weeks until the gorillas weigh the same amount.
