A towns population increased by 1200 people and then this new population decreased 11% the town now had that it to less people than it did before the 1200 increase find the original population
Answers
Answer:
Let the original population of the town be x.
So, we have the population of the town after 1200 people increase is equal to x+1200.
Now the number of people decreased in the town
due to 11% is
(x + 1200)
x + 1200
11x
100 x 11 = 100 + 132
Hence the population after 11% is
11x
x + 1200 132= 89x + 1068
100
100
Since the population after 11% decrease is 32 less than the original population, we have
89x
100
+ 1068 = x - 32
Adding 32 on both sides, we get 89x + 1068 + 32 = x - 32 +32
100
89 100 + 1100 = x
89x 100 Subtracting from both sides, we get
89x
100
+ 1100
» 1100
89x 89x 100
100
11 x
100
Multiplying both sides by 100, we get
11x = 110000
Dividing both sides by 11, we get x=10000
Hence the original population of the town was 10000.
Note: While solving the linear equation if the value of x was fractional and not integral and positive, then the situation described in question was not possible and hence no such value of population existed. This is because the population of a place is
always >0 and an integer. The statement
"Population of a place is 11.5" is meaningless and absurd.