Question

What is the percent of decrease from 110 to 77?

Answer 1

The decrease is `30%.`

Explanation:

Let's start by asking ourselves a similar, yet simpler, question: what is the percent decrease from $10.00 to $9.00? In other words, if a $10 item is sold for $9, what percent did the buyer save?

This seems a bit more intuitive. The answer is 10%. But how did we get that? Well, we figured out the difference between the two prices (`$10 - $9`, which is `$1`), and then compared this difference to the original price of `$10`, and found that `$1` was 10% of `$10`.

This is the math we did in our head:

`("original value "-" new value")/"original value"`

We measured how big the difference between the two numbers is, when compared to the original number. This formula works all the time, to find percentage increases/decreases. Just plug and chug!

In this question, the original value is 110, and the new value is 77:

`(110-77)/110=33/110`

`color(white)((110-77)/110)=0.3`
`color(white)((110-77)/110)=30%`

(To turn a decimal number into a percentage, multiply the number by 100, then add the % sign.)

Answer 2

`30%`

Explanation:

Any percent increase or decrease can be determined by using the process:

`color(red)("change"/"original" xx 100%)`

The change is the amount of increase or decrease, simply subtract:
Bigger value - smaller value.

In this case: `" "110-77 = 33`

Multiplying by `100%` is the same as multiplying by `100/100`, which is equal to `1`. This does not change the value of a number, simply what it looks like. The `%` sign is used in the answer.

`(110-77)/110 xx 100%`

`=33/110 xx 100%`

`=30%`