SOLUTION: Please help me solve this problem, thank you!!the population of manchester is 4 times the population of dover, and the population of portsmouth is 5,650 less than dover. If the pop
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Question 101400: Please help me solve this problem, thank you!!the population of manchester is 4 times the population of dover, and the population of portsmouth is 5,650 less than dover. If the population of all three towns is 154,850, what is the population of each city??
Found 2 solutions by stanbon, doukungfoo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the population of manchester is 4 times the population of dover, and the population of portsmouth is 5,650 less than dover. If the population of all three towns is 154,850, what is the population of each city??
-------------------
Let population of dover be "x"
Manchester = 4x
Portsmouth = x-5650
---------
EQUATION:
x + 4x + x-5650 = 154,850
6x = 169500
x = 26750 (population of Dover)
4x = 107000(population of Manchester)
x-5650 = 21100 (population of Portsmouth)
==============
Cheers,
Stan H.
Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
Lets set Dover's population equal to x
So..
Dover's pop. = x
Now define Manchester's population in terms of x
Given: pop of Manchester is 4 times pop of Dover
Manchester's pop = 4x
Next define Portsmouth's pop in terms of x
Given: pop of Portsmouth is 5650 less than pop of Dover
Portsmouth's pop = x - 5650
Now given that the pop of all three towns is 154850 we can write an equation to solve for x
Ok so...
(Dover pop) + (Manchester pop) + (Portsmouth pop) = 154850
combine like terms
isolate terms with x
solve for x by dividing both sides by 6
Ok so we have our first answer
Answer: Dover's population is 26750
Now we can find the pop for Manchester and Portsmouth
Manchester's pop = 4x
replace x with 26750
4x
4*26750
107000
Answer: Manchester's population is 107000
Now find Portsmouth pop
Portsmouth's pop = x - 5650
replace x with 26750
26750 - 5650
21100
Answer: Portsmouth's population is 21100
Check all answers:
(Dover pop) + (Manchester pop) + (Portsmouth pop) = 154850
26750 + 107000 + 21100 = 154850
154850 = 154850
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