# What is the current population of the town?The projected cost of a new high school is $20,066,340 of which $5,216,340 will be covered by annual grants. Using data from the last census the planning...

What is the current population of the town?

The projected cost of a new high school is $20,066,340 of which $5,216,340 will be covered by annual grants. Using data from the last census the planning committee estimated the cost per town resident. However new census data reveals that the population has increased by 2200 people reducing the cost of each resident by $75.

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### 1 Answer

The projected cost of the new high school is $20066340 of which $5216340 is covered by annual grants. The rest is to be collected from the people of the town. This is equal to $14850000.

Let the actual population of the town be N. The amount required from each person is equal to `14850000/N` . The population of the town according to the earlier census was 2200 less and this increased the amount required from each person by $75. This gives:

`14850000/N-14850000/(N+2200)=75`

=> `(N+2200) - N = N*(N+2200)/198000`

=> `N*(N+2200) = 435600000`

Solving the equation gives two roots 19800 and -22000. As the population cannot be negative, ignore the negative root.

**The population of the town is 19800**