Real Life Problem writing equation

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ksmart

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I am selling t-shirts (for example) for $25.00 INCLUDING tax 0.0725 and INCLUDING shipping fee of $2.50. need to know the actual selling price of the shirts before tax and shipping
I've tried several approches but don't come up with a figure that makes sense. I would like to know the equation.
Thanks in advance
 
Pick a variable for the listing price.

Write an expression for the tax on that price.

Write an expression for the sum of the price, the tax on that price, and the shipping charge.

Set the sum equal to the given total amount.

Solve for the variable.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

Edit: Ne'mind. Complete solution posted below.
 
Hello, ksmart!

You're selling T-shirts and you don't know your own selling price? . . . Heh!

I'm selling t-shirts (for example) for $25.00, incdluding 7.25% tax and $2.50 S&H.
Need to know the actual selling price of the shirts before tax and shipping.
Click to expand...

Excluding shipping and handling, the shirt cost: \(\displaystyle \,\$25.00\,-\,2.50 \:=\:\$22.50\)

Let \(\displaystyle x\) = cost of the shirt.

\(\displaystyle \underbrace{\$22.50}_\downarrow\:\underbrace{\text{is}}_\downarrow\:\underbrace{\text{the shirt}}_\downarrow\:\underbrace{\text{plus}}_\downarrow\:\underbrace{7.25\%\text{ of the shirt}}_\downarrow\)
\(\displaystyle \;22.50 \;= \;\;\;\;\;x\;\;\;\;\;\;+\;\;\;\;\;\;\;\;0.0725x\)

We have the equation: \(\displaystyle \:1.0725x \:=\:22.50\;\;\Rightarrow\;\;x\:=\:\frac{22.50}{1.0725} \:=\:20.97902098\)

Therefore, the cost of the shirt is: \(\displaystyle \,x\:=\:\fbox{\$20.98}\)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Check: The shirt costs $20.98

Tax is: \(\displaystyle 0.0725\,\times\,20.98 \:=\:1.52105 \:\approx\:$1.52\)

Hence: . $20.98 .shirt
. . . . . . . . 1.52 .tax
. . . . . . --------
. . . . . . . 22.50 .subtotal
. . . . . . . . 2.50 .S&H
. . . . . . --------
. . . . . . $25.00 .Total . . . . There!

 
I know, I know - doing it a little backwards -
thanks for the help - I almost had it and see my mistake
ksmart
 
Check carefully the laws in your location. They may require you to charge tax on the Shipping and Handling. That would make for a slightly different solution.
 
I am struggling with these problems. It's been 40 years since I had to do anything like this and now I have to take a test on it. I don't understand all the x+y=(k-2) stuff. Can you explain this problem in simple English? Where did you get 1.0725?

The original problem:
I'm selling t-shirts (for example) for $25.00, incdluding 7.25% tax and $2.50 S&H.
Need to know the actual selling price of the shirts before tax and shipping.

Thanks, Grammy
 
The price of the item is the first "1" or 100% of the price.

The tax on the item is the ".0725" or 7.25% of the price.

Add them together to produce, "1.0725", or 107.25% of the price, or the price includign tax.
 
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