Word Problem

[m2bma]

If a television costs $116 after a 10% disocunt, what was the original cost? Need formula to show work. Thanks!

 

[tkhunny]

You do NOT need "formula to show work". Taht would be no work. You need to define your problem and solve it.

Definition: X = Original Cost

You tell me what's next.

 

[m2bma]

X = X10%
10% DISCOUNT - ORIGINAL PRICE OF THE TV

 

[tkhunny]

What? Look really hard at what you wrote.

X = X10%

First, that doesn't mean anything.
Second, if you meant X = X*10%, the ONLY solution is X = $0.00. No good.

Hint:
Discount = (Original Price)*(Discount Rate)

 

[m2bma]

I KNOW I HAVE TO FIND THE ORIGINAL PRICE. SO, I WOULD TAKE THE ORIGINAL PRICE TIMES 10% AND THAT WOULD GIVE ME THE 10% DISCOUNT. THEN, I WOULD TAKE THE ORIGINAL PRICE AND SUBSTRACT THE 10% DISCOUNT. THAT WOULD GIVE ME THE $116, BUT I DON'T KNOW HOW TO GET THE ORIGINAL COST.

 

[soroban]

Hello, m2bma!

If a television costs $116 after a 10% discount, what was the original cost?

Give it some thought . . .

If you get a 10% discount, then you are paying 90% of the original cost.

That is: 90% of the original cost is $116.

And there is your equation: \(\displaystyle \:0.90\cdot X\;=\;116\)

 

[m2bma]

Thank you! It makes so much more sense now. So easy....but made it so hard.

 

[tkhunny]

No, you didn't make it hard. You described it perfectly. Just make your notation do that.

X = Original Price
X * 10% = Discount

(Original Price) - (Discount) = (Discounted Price)

X - X*10% = $116

Now, a little algebra:

X*(1 - 10%) = $116
X*(1 - 0.10) = $116
X*(0.90) = $116
X = $116/0.90