MATH: If I bought something for $23.43 after 20% off, how much was it before the discount?

To create the discount, you had multiplied the original price by .8, so to make it before the discount, just divide it by .8.

23.43 / .8 = 29.29

Answer is $29.30, and here's how I got it:

1) Convert 20% to a fraction: 1/5

We now know that $23.43 is 4/5 of the amount we're trying to figure out

2) Figure out the amount of money that 1/5 would be. Do this by dividing $23.43 by 4 (since it makes up the 4 remaining parts)

We get $5.86

3) Multiply all 1/5's together. Each 1/5 is $5.86 so we multiply that by 5

We get: $29.30

To check our work, we should find what 80% (100% minus the 20%) is.

29.30 x .80 = $23.44

Now the reason we got $23.44 instead of $23.43 is because I rounded the decimals off when I did this. It is acceptable be off by one cent because of that (some people round, some people don't; either is okay)

20% off means that the total, x - (20% of x) = $23.43

80% = .8

So .80 * x = $23.43

x = $23.43 / .8

x = $29.29

x - 0.2x = $23.43

0.8x = 23.43

[now divide both sides by 0.8 to isolate x]

x = 23.43/0.8 = $29.2875 which rounds up to $29.29

X - X(.2) = 23.43

.8X = 23.43

X = 23.43/.8

X = 29.28