sales tax: Total cost of chair, including 7% Tax A and 7% Tax B, is $102.60.

[steveopolis]

In an exercise on 'Percent Applications - Sales Tax' I know how to figure out:
*tax amount if I know tax rate (percent) and purchase price
*purchase price if I know tax rate and tax amount paid
*tax rate if I know purchase price and tax amount paid

For 7/8 questions, the method we were taught works easily. e.g.
Taxrate x purchaseprice / 100x

But this one I don't know how to do, even when I see the answer key says $90:

"Total cost of chair, including 7% Tax A and 7% Tax B, is $102.60.
What is the purchase price of the chair?"

We'd be expected to use the same method as above, though a preceding step of adding or subtracting any given variable is also permitted.

 

[Dr.Peterson]

In an exercise on 'Percent Applications - Sales Tax' I know how to figure out:
*tax amount if I know tax rate (percent) and purchase price
*purchase price if I know tax rate and tax amount paid
*tax rate if I know purchase price and tax amount paid

For 7/8 questions, the method we were taught works easily. e.g.
Taxrate x purchaseprice / 100x

But this one I don't know how to do, even when I see the answer key says $90:

"Total cost of chair, including 7% Tax A and 7% Tax B, is $102.60.
What is the purchase price of the chair?"

We'd be expected to use the same method as above, though a preceding step of adding or subtracting any given variable is also permitted.

This is a case where I'd like to look at your book or notes to see more precisely what methods are being taught. There are two main ways to do this kind, which are commonly taught in algebra classes and in pre-algebra classes, respectively.

First we can use fairly simple algebra. Define the unknown purchase price as a variable x, and write an equation following the rules you have learned, showing how the known total cost would be calculated if you knew x. Then you can solve for x.

Second, if you aren't comfortable enough with algebra, you can do the equivalent by doing a little extra thinking. If you add 7% of the price, and another 7% of the price, to the price itself (100% of the price!), then the total is 100% + 7$ + 7% of the price. Then you can find the price, knowing that this total percent of it is $102.60.

Try one of those methods, and show us what you can do.

Another thing that may help you is to turn the problem around, since you have the answer. Suppose you knew the price was $90; how would you find the total amount spent after adding 7% and 7% taxes? This will check that the answer is correct, and also give you a bit of a feel for what is happening in the problem, which may help you in thinking about either of the methods I described. This is often a good way to approach an unfamiliar problem -- even if you have to make up an "answer" just to experiment with it.

 

[steveopolis]

Ah!!! Wonderful!!

From your response, I could understand that $102.60 is 114% of the purchase price, so:

102.60/x = 114/100

(In my notebook, I format them as vertical fractions, then cross multiply.)

102.60 x 100 = 10260
10260 = 114x
10260 / 114
x = 90

That fits with the method we've been taught so far.

Thank you again, Dr.Peterson!

 

[steveopolis]

ha, in the very next section of the course, they introduced the above! They still didn't *teach* it, they just said, "This course did not provide information on how to do this, but give it a try." Because of your help, Dr.Peterson, I was able to do it

The course often teaches something 1-8 modules after first asking us to solve it. I don't know why they do it this way -it can only serve to frustrate us. But not anymore, now that I found this forum!

 

[Steven G]

Another way:
total tax = .07 + .07 = .14

purchase price = 102.60 / 1.14 = 90

I see that you have been practicing. Last week you did not know what 7 + 7 was. Good job. Someday you will get it all!

 

[steveopolis]

Another way:
total tax = .07 + .07 = .14

purchase price = 102.60 / 1.14 = 90

Thanks, Denis