Question

Please help. I’m so confused... I went to the mall and bought a shirt on sale for $30. I paid 75% of the original price. What was the original price of the shirt?

Answer 1

The original price was `$40`.

Explanation:

`0.75*x = 30`

where `x` equals the original price of the shirt.

Since `75%` (or `0.75`) times the original price of the shirt (`x`) gives you `$30`, you need to solve for `x`.

By doing this, you get `x = 30/0.75= 40`.

Therefore, the original price of the shirt was `$40`.

Answer 2

$40

Explanation:

your `$30=75%` so divide both numbers by 75 and this will give you the value of 1%. Then multiply by 100 to find the original price.

`30/75=2/5`

`2/5 xx 100 = 40`

Answer 3

`$40`

Explanation:

This is an example of what is called 'reverse percentage'.

The problem is that you do not know the original price and the `25%` discount that was given was calculated on that unknown value.
A common error is for students to calculate `25%` of the sale price and add it on again. However, `25%` of a bigger number and `25%` of a smaller value are not the same.

The easiest method is to write a proportion comparing the percentages (which you know) with the prices.

`$30` corresponds with `75%`
`$???` corresponds with `100%" "`(ie the original price)

`x/100 = 30/75" "larr` multiply by`100` to find `x`

`x = (30xx100)/75`

`x = $40`

You could also use algebra to write and solve an equation, but the maths is horrible! Rather use the direct proportion method for percentage calculations.

Answer 4

See a solution process below:

Explanation:

We can rewrite the question as:

$30 is 75% of what?

"Percent" or "%" means "out of 100" or "per 100", Therefore 75% can be written as `75/100`.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the price we are looking for "p".

Putting this altogether we can write this equation and solve for `p` while keeping the equation balanced:

`$30 = 75/100 xx p`

`color(red)(100)/color(blue)(75) xx $30 = color(red)(100)/color(blue)(75) xx 75/100 xx p`

`($3000)/color(blue)(75) = cancel(color(red)(100))/cancel(color(blue)(75)) xx color(blue)(cancel(color(black)(75)))/color(red)(cancel(color(black)(100))) xx p`

`$40 = p`

`p = $40`

The original price of the shirt was $40.