# How to work out this discount?

Accommodation at a hotel is $1170. The owner agrees to give a 12% discount to someone. How do you get the answer? Attempt I did: 1170/1.12 I have been told that this is wrong. In which situations would use use this method of dividing over the method where you times it by 0.12 then subtract that amount from the original amount? Thanks. • If by "answer" you mean the price after the discount, then it's $$1170 - (0.12 \times 1170)$$ Nov 25, 2016 at 22:20 ## 4 Answers If you knew that a price had been increased by$12\%$and was now \$1300, then you would divide by $1.12$ to get the original price.

For your problem, the price has been decreased by $12\%$, so $(0.12)*1170$ has been subtracted. That's the same as multiplying by $1 - 0.12 = 0.88.$ In my example above, $12\%$ is added, so we multiply by $1+0.12$. You would divide if you were reversing either of these.

For your question you would multiply the initial price of 1170 by 0.12, then subtract that amount from the initial price to get the total price after the discount is applied..

So the discount is

 1170*.12
= 140.4


Then, the total price after the discount is just

 1170 - 140.4
= 1029.6


12 % discount means 12/100 part of initial amount. So if the person is getting a discount of 12% then he will save $(12/100)1170$ which is 140.4$maybe think of it this way: You have a numbert to start with, the$\$1170$. Now decide if you are looking for the value before, or after the discounting / increase event.

Let's deal with the after case:

I need the value after increase or decrease, so I need to add or subtract proportion of what I have, to what I have, to get the value after: $$\mathrm{value \;after}=1170\cdot(1+0.12)=1310.4\;\;[increase\;case]$$ $$\mathrm{value \;after}=1170\cdot(1-0.12)=1029.6\;\;[discount\;case]$$

The second line is the calc needed for your question, because you were looking for the value after a discount.

Now let's deal with the before case (here the price change has happened, and I want to reverse its effect to find out where I started:

$$\mathrm{value \;before}=\frac{1310.4}{1+0.12}=1170\;\;[increase\;case]$$ $$\mathrm{value \;before}=\frac{1029.6}{1-0.12}=1170\;\;[discount\;case]$$

Hope that helps?