Question

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

Answer 1

`$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

Answer 2

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`