Brothers Petros, Filmon and Yonas agreed to spend the following amount for present for mom. Petros $80 more than Filmon. Yonas paid $220 more than the total paid by the two. If Yonas paid $480 more than Petros how much was the present?

Let us assume Filmon paid `$x` and therefore Petros paid `$(x+80)`.

So two together paid `$x+$(x+80)` i.e. `$(2x+80)`.

Hence, Yonas paid `$(2x+80)+$220=$2x+300`, which was `$480` more than Petros, who had paid `$(x+80)` i.e.

`2x+300=x+80+480=x+560`

Hence, `2x-x=560-300` or `x=260`.

Hence Filmon paid `$260`

Petros paid `$260+$80=$340` and

Yonas paid `$(2xx260+300)=$(520+300)=$820`

Hence, present costs `$2360+$340+$820=$1420`

Before we can start comparing how much each spent, we need to define a variable to use.
Filmon paid the least.

Let the amount Filmon paid be `x`

Write an expression for how much each of them paid, in terms of `x`

Filmon paid: `x" "` Petros paid $80 more: `x+80`

Yonas paid `220` more than both together:

Yonas: `(x+x+80)+220 = 2x+300`

The difference between Yonas' and Petros' payments is $480

`"(biggest - smaller" = $480)`

`2x+300 -(x+80)= 480`

`2x+300-x-80 = 480`

`x = 480-300+80`

`x =$260`

Filmon paid `$260`
Petros paid: `260+80 = $340`
Yonas paid `2 xx 260+300 =$820`

The cost of the present was:

`$260+$340+$820`

`$1420`