Question
The population of Linton is 12 times as great as the population of Ellmore. The combined population of both towns is 9,646 people. What is the population of Linton?
Ask by Blake Dawson. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The population of Linton is 8,904 people.
Solution
Let the population of Ellmore be E. Then the population of Linton is 12E. According to the problem, their total population is:
E + 12E = 9,646
Combining like terms gives:
13E = 9,646
Now solve for E:
E = 9,646 ÷ 13
E = 742
Since Linton's population is 12 times that of Ellmore, we have:
Linton = 12 × 742 = 8,904
Thus, the population of Linton is 8,904 people.
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Simplify this solution Beyond the Answer
To find the population of Linton, we can use algebra. Let the population of Ellmore be represented as \( x \). Then the population of Linton would be \( 12x \). According to the problem, the combined population of both towns is 9,646 people. Therefore, we can set up the equation: \[ x + 12x = 9,646 \] This simplifies to: \[ 13x = 9,646 \] Now, divide both sides by 13 to find \( x \): \[ x = \frac{9,646}{13} = 743 \] Now that we have the population of Ellmore, we can find Linton's population: \[ Linton = 12x = 12 \times 743 = 8,916 \] So, the population of Linton is 8,916 people.
