$120 is divided among the certain number of children.if there were 3 child more each would've receved $2 less.

Question

then find the number of children

Answer 1

120 / 10 children= $12.............120 / 13= $9.23..............nope
120 / 11 children= $10.91........120 / 14= $8.57..............nope
120 / 12 children= $10.............120 / 15= $8...................yep


there's 12 children and they would recieve $10 each, but if there were 3 more(15 children) they would only recieve $8($2 less)

Answer 2

Let the number of children be x.

120/x (Original number)
120/x+3

Difference: Each received $2 less.

Equation:
$120 $120
--------- - -------- = $2
x x+3

Work out the equation :

$120(x+3) $120(x)
------------- - ---------- = $2
x(x+3) x(x+3)

Calculate:

120x+$360 120x
-------------- - --------- = $2
x(x+3) x(x+3)

That will give you:

120x+$360-$120x
------------------------ = $2
x(x+3)

(Cancel the two 120x as they become 0 after calculation.)

That will give you:

360
-------- = $2
x(x+3)

(Expand the denominator)

360
------- = $2
x*2+3x

(Multiply $2 with the expanded denominator.)


You will get:

360
-------
2x*2+6x

You can then get the equation: 2x*2+6x-360=0

Factorise and you will get: (x-12) and (2x+30)

Therefore: x=12 or 2x=-30
x=12 or x=-15

(You will get 2 answers, 12 and minus 15, but since x cannot be negative logically, x has to be 12.)

It is a long step but it is a sure way.Hope this helps!!Good Luck!!

Answer 3

Or,
120/x = y
120/(x+3) = y - 2
Substitute first equation into the second.
You get -2x^2 - 6x + 360 = 0
Use the quadratic formula and get x = 12

Answer 4

this can be solved using algebra and the formula for a quadratic equation

($120/x) - [$120/(x+3)] = $2

([120*(x+3)]/[x*(x+3)]) - ((120*x)/[x*(x+3)]) = 2

[(120*x + 360) - 120*x]/[x*(x+3)] = 2

360/[x*(x+3)] = 2

180 = x*(x+3) ... x^2 + 3x -180 = 0

for quadratic equations of the form x^2 + bx + c = 0

x = (b^2 ± SQRT(b^2 - 4ac)) / 2a

using this formula, x = 12