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$50

Explanation:

We should start off by making an equation.

(0.8)x=40(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 0.80.8 or multiply 40 by 5/454 (because 4/545 is 80%) .

You should get 200/42004 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$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 xx

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)d$40ddd=dddxdddddddd20100x

This is the same as:

color(green)($40=80/100 x)$40=80100x
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Shortcut method")Shortcut method
Note that the shortcut method is just remembering the end effect of first the principle method

$40=80/100x$40=80100x

Move the 80/10080100 to the other side of the = but turn it upside down giving:

$40xx100/80=x$40×10080=x

x=$50x=$50

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

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

If we can turn the 80/10080100 into 1 then 1xx x=x1×x=x so we get xx on its own.

Multiply both sides by color(red)(100/80)10080

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) )$40=80100xdddbecomes ddd$40×10080dd=dd80100x×10080

but 80/100xx100/80 =180100×10080=1

color(white)("ddddddddddddddddddd")->color(white)("ddd")color(green)(40/80xx100color(white)("d")=color(white)("d")x)dddddddddddddddddddddd4080×100d=dx

color(white)("dddddddddddddddddddd")->color(white)("ddd")color(green)(1/2xx100color(white)("d")=color(white)("d")xcolor(white)("d")=50)ddddddddddddddddddddddd12×100d=dxd=50

But this is in dollars

Original price was $50.00$50.00