successive discounts: requesting examples
- Thread starter ekatz
- Start date
Re: successive discounts
Perhaps it would be better if you would give US an example of a question you're having trouble with. Then we can see exactly what you're dealing with. Otherwise, we are just guessing....which may not prove useful.
ekatz said:can anyone give me an example of one? I'm having a tuff time trying to figure out how to do them.
Perhaps it would be better if you would give US an example of a question you're having trouble with. Then we can see exactly what you're dealing with. Otherwise, we are just guessing....which may not prove useful.
Hello, ekatz!
I'm sure I understand what you mean . . .
Example: A car sells for $8000.
We are given successive discounts of 20%, 15%, and 10%.
What is the final discounted price?
Important: Do not add the discounts!
We can take the discounts one-at-a-time.
. . This takes a while, but it illustrates exactly what is going on.
We get a 20% discount on $8000: \(\displaystyle \:0.20\,\times\,8000\:=\:1600\)
. . The sale price is: \(\displaystyle \:\$8,000\,-\,1600\:=\:\$6,400\)
We get a 15% discount on $6,400:\(\displaystyle \:0.15\,\times\,6400\:=\:960\)
. . The new sale price is: \(\displaystyle \:\$6,400\,-\,960\:=\:\$5,440\)
We get a 10% discount on $5,440: \(\displaystyle \:0.10\,\times\,5440 \:=\:544\)
. . The final sale price is: \(\displaystyle \:\$5,400\,-\,544\:=\:\L\fbox{\$4,896}\) . . . There!
There is a faster way.
Consider the percentage that we pay.
With a 20% discount, we pay 80% of the original price.
With a 15% discount, we pay 85%.
With a 10% discount, we pay 90%
These percents can be combined: multiply.
We have: \(\displaystyle \;0.80\,\times\,0.85\,\times\,0.90\;=\;0.612\;\) **
The final sale price is: \(\displaystyle \:0.612\,\times\,\$8,000\:=\:\L\fbox{\$4,896}\) . . . see?
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
**
We see that we pay: \(\displaystyle \,0.612 \:=\:61.2\%\) of the $8,000.
This means that we had a \(\displaystyle 38.8\%\) discount
. . . and not the 45% we'd get if we added the discounts.
I'm sure I understand what you mean . . .
Example: A car sells for $8000.
We are given successive discounts of 20%, 15%, and 10%.
What is the final discounted price?
Important: Do not add the discounts!
We can take the discounts one-at-a-time.
. . This takes a while, but it illustrates exactly what is going on.
We get a 20% discount on $8000: \(\displaystyle \:0.20\,\times\,8000\:=\:1600\)
. . The sale price is: \(\displaystyle \:\$8,000\,-\,1600\:=\:\$6,400\)
We get a 15% discount on $6,400:\(\displaystyle \:0.15\,\times\,6400\:=\:960\)
. . The new sale price is: \(\displaystyle \:\$6,400\,-\,960\:=\:\$5,440\)
We get a 10% discount on $5,440: \(\displaystyle \:0.10\,\times\,5440 \:=\:544\)
. . The final sale price is: \(\displaystyle \:\$5,400\,-\,544\:=\:\L\fbox{\$4,896}\) . . . There!
There is a faster way.
Consider the percentage that we pay.
With a 20% discount, we pay 80% of the original price.
With a 15% discount, we pay 85%.
With a 10% discount, we pay 90%
These percents can be combined: multiply.
We have: \(\displaystyle \;0.80\,\times\,0.85\,\times\,0.90\;=\;0.612\;\) **
The final sale price is: \(\displaystyle \:0.612\,\times\,\$8,000\:=\:\L\fbox{\$4,896}\) . . . see?
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
**
We see that we pay: \(\displaystyle \,0.612 \:=\:61.2\%\) of the $8,000.
This means that we had a \(\displaystyle 38.8\%\) discount
. . . and not the 45% we'd get if we added the discounts.