Allison Welch bought a computer game for $40. The game was discounted 20%. What was the regular price of the game?

2 Answers
Oct 20, 2017

#$50#

Explanation:

We should start off by making an equation.

#(0.8)x=40#.

x is the original price of the game, and 80% of the original or 20% off of the original.

We then divide both sides by #0.8# or multiply 40 by #5/4# (because #4/5# is 80%) .

You should get #200/4# or 50 therefore the answer is 50.

Plug in 50 into the equation and you should get 40.

-Sakuya

Oct 20, 2017

Original price was #$50.00#

Explanation:

For an in-depth explanation of what percentage is see this example:
https://socratic.org/s/aK9mhH3Z

Let the original price be #x#

Then:

new price = original price - 20% of original price
#color(white)("d")color(green)( $40 color(white)("ddd")= color(white)("ddd")xcolor(white)("dddd")-color(white)("dddd")20/100 x)#

This is the same as:

#color(green)($40=80/100 x)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method")#
Note that the shortcut method is just remembering the end effect of first the principle method

#$40=80/100x#

Move the #80/100# to the other side of the = but turn it upside down giving:

#$40xx100/80=x#

#x=$50#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("First principle method")#

If we can turn the #80/100# into 1 then #1xx x=x# so we get #x# on its own.

Multiply both sides by #color(red)(100/80)#

So # color(green)($40=80/100 x color(white)("ddd") color(black)("becomes ") color(white)("ddd")$40color(red)(xx100/80)color(white)("dd")=color(white)("dd")80/100xcolor(red)(xx100/80) )#

but #80/100xx100/80 =1#

#color(white)("ddddddddddddddddddd")->color(white)("ddd")color(green)(40/80xx100color(white)("d")=color(white)("d")x)#

#color(white)("dddddddddddddddddddd")->color(white)("ddd")color(green)(1/2xx100color(white)("d")=color(white)("d")xcolor(white)("d")=50)#

But this is in dollars

Original price was #$50.00#