Whats the equation ?

Question

After 45% price reduction , you purchase a digital camera for$276.What was the original price of the camera ?

Answer 1

Hi Melony,

Some people get sucked into the error of taking 45% of the sale price and adding it on to get the original price. This is wrong because the 45% was applied to the original price, which you don't know yet! However, you can find it by asking the question "45% of what number, when subtracted from that number, results in $276?"

In mathematical terms, this statement is x - .45x = $276

Undistributing the common factor x, (1-.45)x = $276

.55x = $276

x = $276/.55 = $501.82, to the nearest penny

Answer 2

Hey Melony,

Hope you're doing well. The way to think about this is to first set up an equation using words, then convert everything to variables.

So, if you're taking a 45% discount on a camera, you would first ask yourself, what's 45% of that initial price? To find 45% of something, you can multiple that price by .45 or 45/100, which is the way to convert percentages (Also, anytime you see the word "of", think multiply).

After finding that number, you would take the real price and subtract the discount. So, maybe something like INITIAL PRICE - (INITIAL PRICE × .45) = FINAL PRICE.

Now, just set up variables for all this. I = Initial Price and the final price you already know to be $276.

So, I–.45 I= 276. Now, I–.45I = .55I. This is no different than subtracting 5x-3x to get 2x. Just imagine there is a 1 in front of the first I.

Now, the final step. .55I=276, so divide both sides .55 to get I by itself. I = 276/.55 = 501.82. That's your final price.

Hope this helps!