sales tax

[lev888]

These are your steps for solving my problem:

1. 5% = 0.05 I convert tax percentage into a decimal by moving the decimal point two spaces to the left. 5%= 0.05

2. I multiply the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax. 20* 0.05=1

3. Add the sales tax value to the pre-tax value to calculate the total cost. =21. I am paying $21.

Do you see that your problem is the "reverse" of mine? If you know how to find the total by following the steps above, you should be able to do the reverse - find the tax based on the total and pre-tax price:
1. find the tax amount,
2. the tax in decimal form,
3. the tax as %.

 

[Steven G]

You found that t= 1.0686 which is correct. Now can you explain why you subtract the 1 from 1.0686 to get your final answer of .0686= 6.86%? Now you did not make any mistakes I just want to be sure that you understand why you subtract the 1.

 

[pka]

Dear friends and teachers:
This one looks easier, but for me, not quite so easy.
A company dropped the price of the laptop by 15%. The original price of the laptop was $845 and the price the customer paid after sales tax was $767.53. Which of the following is closest to the sales tax paid by the customer?.
a. 6%______b. 6.5%______c.7%______d. 8%______e. 8.5%

This entire thread bothers me in the extreme.
Here is a formula for percent of price change: \(\dfrac{N_p-O_p}{O_p}\).
That says "New price minus old price divided by old price.
Now whether that result is positive/negative means an increase/decrease.
Now let's look at this particular problem the \(O_p=845\) and the discount is \(0.15\).
So \(\dfrac{N_p-845}{845}=-0.15\) OR \(N_p=718.25\)SEE HERE
Now to find the sale tax \(\dfrac{767.53-718.25}{718.25}\approx0.069\) SEE HERE

 

[eddy2017]

You found that t= 1.0686 which is correct. Now can you explain why you subtract the 1 from 1.0686 to get your final answer of .0686= 6.86%? Now you did not make any mistakes I just want to be sure that you understand why you subtract the 1.

I didn't. That is where I was stuck.
Then Kahn provided a different equation where I had no 1 as a result.
But I think my equation was right too.
Only that I didn't know how to proceed from that
1.0686 which was nowhere near any of the answer choices.

 

[lev888]

The reason I keep pushing the connection between the original problem and the one I posed: you may learn how to solve the 'find tax' problem. Now you remember 2 methods. Then you'll encounter a 'find the pre-tax price' problem and will learn another method. 3 methods now.
Instead, you should remember the relationship between the quantities involved and use it as needed.

 

[eddy2017]

Hey, lev888, I can't wait to do it that way, but the reverse thing is throwing me off. Can you send any hint as to first step to do it.

 

[eddy2017]

This entire thread bothers me in the extreme.
Here is a formula for percent of price change: \(\dfrac{N_p-O_p}{O_p}\).
That says "New price minus old price divided by old price.
Now whether that result is positive/negative means an increase/decrease.
Now let's look at this particular problem the \(O_p=845\) and the discount is \(0.15\).
So \(\dfrac{N_p-845}{845}=-0.15\) OR \(N_p=718.25\)SEE HERE
Now to find the sale tax \(\dfrac{767.53-718.25}{718.25}\approx0.069\) SEE HERE

Uhmm, that is quite interesting, pka. I liked that way a lot. Thank you.

 

[lev888]

Hey, lev888, I can't wait to do it that way, but the reverse thing is throwing me off. Can you send any hint as to first step to do it.

Let's forget about the reverse (btw, I think the right term is inverse, sorry).

Here's the relationship in terms you are familiar with (you used it to solve my problem):
Total price = pre-tax price + pre-tax price * tax (in decimal form)

Makes sense?
So, for any problem asking for the total price you can plug in the pre-tax price and the tax in the formula above and calculate the total.
What about your problem? SAME THING. Plug in the pre-tax price and total price. What do you get? An equation, where the tax is the unknown. Solve it and you got your tax - just in decimal form. But you know how to convert it to the percentage form.
What about the remaining category of problems where the pre-tax price is unknown? Same thing as above - plug in known values, solve the equation.

 

[Steven G]

Uhmm, that is quite interesting, pka. I liked that way a lot. Thank you.

No, no , no. Liking the formula is not enough. You need to understand and like the formula. Liking is however not necessary but understanding it is important.

Do you understand the formula? If you do then you'll have it for life. Otherwise it will only be useful for this single problem.

Now I am not bashing pka or you. I like this formula and personally have used it to do these problems for myself. I get to use it because I understand it! You too should use it but not before understanding it. One reason students hate math and/or do poorly in it is because they may be able to do the early math problems but do not understand why their method works. Then when problems come up requiring understanding many say that they do not understand these problems.

 

[eddy2017]

I agree with you totally. Well, I will study it more deeply. And if you hava problem where I can apply it, let me know.

 

[Steven G]

I agree with you totally. Well, I will study it more deeply. And if you hava problem where I can apply it, let me know.

If you understand the formula then you'll know when/where to apply it. No one should need to tell you.

If I tell you that I have three apples and Jose gives me two more apples. If I ask you how many apples I now have you know immediately to add. You need to know immediately when to use the formula quoted by pka.

 

[eddy2017]

I see that there are many ways to solving this problem, but I would love to know how I could go from,in my first answer, which according to Jomo is correct, 1.0686], how can I substract the 1, and why?.

 

[eddy2017]

Ok, thanks, Jomo.Yes, you're right.

 

[eddy2017]

Let's forget about the reverse (btw, I think the right term is inverse, sorry).

Here's the relationship in terms you are familiar with (you used it to solve my problem):
Total price = pre-tax price + pre-tax price * tax (in decimal form)

Makes sense?
So, for any problem asking for the total price you can plug in the pre-tax price and the tax in the formula above and calculate the total.
What about your problem? SAME THING. Plug in the pre-tax price and total price. What do you get? An equation, where the tax is the unknown. Solve it and you got your tax - just in decimal form. But you know how to convert it to the percentage form.
What about the remaining category of problems where the pre-tax price is unknown? Same thing as above - plug in known values, solve the equation.

Thanks. I'll do it and send it to you for confirmation.

 

[eddy2017]

Thanks. I'll do it and send it to you for confirmation.

Thanks. I'll do it and send it to you for confirmation.

Total price = pre-tax price + pre-tax price * tax (in decimal form)
767.53(total price) = 718.25 (pre-tax price) + 718.25 * t
767.53(total price) = 718.25 (pre-tax price) + 718.25 t

Before I continue simplifying, is this correctly set up now?.

 

[lev888]

Total price = pre-tax price + pre-tax price * tax (in decimal form)
767.53(total price) = 718.25 (pre-tax price) + 718.25 * t
767.53(total price) = 718.25 (pre-tax price) + 718.25 t

Before I continue simplifying, is this correctly set up now?.

Yes.

 

[eddy2017]

Okay.
isolating t by subtracting 718.25 from both sides.

767.53(total price) = 718.25 (pre-tax price) + 718.25 t
- 718.25 -718.25 (both cancel out)

49.28 =718.25 + t (isolating the unknown by subtracting 718.26 from both sides)

t= -668.97
I multiply times 100 to convert it to percent form =6,689.

Woow!.
Please, may you confirm?.

 

[lev888]

Okay.
isolating t by subtracting 718.25 from both sides.

767.53(total price) = 718.25 (pre-tax price) + 718.25 t
- 718.25 -718.25 (both cancel out)

49.28 =718.25 + t (isolating the unknown by subtracting 718.26 from both sides)

t= -668.97
I multiply times 100 to convert it to percent form =6,689.

Woow!.
Please, may you confirm?.

49.28 =718.25 + t is not correct. Please check.

 

[eddy2017]

How come?.
Can I not subtract 718.25 from both sides?.

 

[lev888]

How come?.

You made a mistake in the previous step.