# A community center being built is expected to cost 1.2 million. Cost per person is increased by 3$ as it's discovered that there's 225 fewer residents than when planning began. What's the new cost...

A community center being built is expected to cost 1.2 million. Cost per person is increased by 3$ as it's discovered that there's 225 fewer residents than when planning began. What's the new cost per resident? Solve using an *algebraic equation*.

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### 1 Answer

Form 2 simultaneous equations .

Let x = the number of people and y = $ amount

xy = 1 200 000 therefore x = `1200000/y`

(x - 225) x (y + 3) = 1 200 000 (now multiply the two brackets)

xy + 3x -225y - 675 = 1 200 000

now substitute the x= from the previous equation so that you only have one unknown (ie y)

`1200000/y` `y` `+ 3 1200000/y- 225y -675 = 1200000`

`1200000 + 3600000/y - 225y - 675 = 1200000` (the 1,2m on either side will cancel each other out )

`3600000/y - 225y - 675 = 0` (multiply by denominator y)

`3600000 - 225y^2 - 675y = 0` (multiply by a negative and rearrange)

`225y^2+ 675y - 3600000 = 0` (divide all by 225 to simplify)

`y^2 + 3y - 16000 = 0` (factorise factors of `y^2` are just (y..) (y..) and factors of 16000 that will fit with our middle factor of 3..(125) (128)

`(y+ 128) (y- 125) = 0`

y = -128 (which it cannot be) OR y = $125Calculate x

**`xy = 1200000` **so `x= 12000000/ 125`

x= 9600people

Now remember these are original values so from these you can calculate:

9600 people originally less 225 x $125 + $3

9375 x 128 = 1 200 000

So the **new cost** per resident** = $128**