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?

2 Answers
Sep 26, 2016

Present costs #$1420#

Explanation:

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#

Sep 26, 2016

#$1420" "# was the cost of the present.

Explanation:

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#