We're told that she paid 8% tax, but if she had paid 5% tax she would have paid $12 less. In other words, 3% tax = $12.

If we know that 3% of the sales price is $12, we can figure out the actual sales price.

3/100 = 12/x
3x = 1200
x = 400

We might be tempted by (c) at this point, but remember step 4 of the Kaplan method for problem solving - double check the question!

We want the price she paid including sales tax. She paid 8% tax, so the actual answer is:

400 + 8%(400) = 400 + 32 = 432: choose (E).

Note that (d) is in there to punish people who did everything right then added 5% sales tax instead of 8%!

II wrote:See attached question:

A) 368
B) 380
C) 400
D) 420
E) 432

E

Stuart Kovinsky wrote:We're told that she paid 8% tax, but if she had paid 5% tax she would have paid $12 less. In other words, 3% tax = $12.

If we know that 3% of the sales price is $12, we can figure out the actual sales price.

3/100 = 12/x
3x = 1200
x = 400

We might be tempted by (c) at this point, but remember step 4 of the Kaplan method for problem solving - double check the question!

We want the price she paid including sales tax. She paid 8% tax, so the actual answer is:

400 + 8%(400) = 400 + 32 = 432: choose (E).

Note that (d) is in there to punish people who did everything right then added 5% sales tax instead of 8%!

Thanks Stuart.

I did it the traditional way. Assign variables and create equations:
p = purchase price
8% tax on purchase = 0.08p
With 5% tax she would pay $12 less in sales tax on purchase. This can be written as: 0.05p = 0.08p - 12

12 = 0.03p
12/0.03 = p
1200/3 = p
400 = p

So purchase price is $400.
8% of $400 is $32 (1% is 4 ... 4*8 = 32)
$400 + $32 = $432 ... answer E.

Another way could be -

Total amount exculding sales tax = x
therefore, 8x/100 - 5x/100 = 12
that gives x = 400 and including 8% sales tax the amount is 432.

II wrote:

Stuart Kovinsky wrote:We're told that she paid 8% tax, but if she had paid 5% tax she would have paid $12 less. In other words, 3% tax = $12.

If we know that 3% of the sales price is $12, we can figure out the actual sales price.

3/100 = 12/x
3x = 1200
x = 400

We might be tempted by (c) at this point, but remember step 4 of the Kaplan method for problem solving - double check the question!

We want the price she paid including sales tax. She paid 8% tax, so the actual answer is:

400 + 8%(400) = 400 + 32 = 432: choose (E).

Note that (d) is in there to punish people who did everything right then added 5% sales tax instead of 8%!

Thanks Stuart.

I did it the traditional way. Assign variables and create equations:
p = purchase price
8% tax on purchase = 0.08p
With 5% tax she would pay $12 less in sales tax on purchase. This can be written as: 0.05p = 0.08p - 12

12 = 0.03p
12/0.03 = p
1200/3 = p
400 = p

So purchase price is $400.
8% of $400 is $32 (1% is 4 ... 4*8 = 32)
$400 + $32 = $432 ... answer E.