After a 20% reduction, a 42-inch HDTV sold for $256. What was the...

Question

After a 20% reduction, a 42-inch HDTV sold for $256. What was the price before the reduction?

Accepted Answer

Hello everybody. Everything right. Today, today, we're going to be looking at this question that states if you buy a bulk of technical handbooks, a 16% discount will be applied and its price will be reduced to $756. And then they ask us to solve for the price of 10 technical handbooks if they are not to be sold in bulk. Now, the extras are provided are a $90 b $900 C $0.5 and the $820. Now, before we get into any math, we can go ahead and eliminate some answers. So they're asking us to solve for the regular price of the books not sold the book. So without a discount, if they tell us that $756 is with a discount, then without a discount, the price has to be more than 756. So we can eliminate answer choice A which is less than that and answer choice C which is also less than that and will be less left with answer choice B and D. Now for that, now we have to get into some math and I'm going to sign a variable and let's say X is equal to the regular price oh 10 technical handbooks. And after we assign that variable, we can go ahead and start making some equations. So if X is the price without any deductions, we'll have that X minus. So the regular price minus 0.16 X and this is I turned the 16% to into a decimal by moving the decimal point to the left twice. So that 16% as a decimal is 0.16. So we have that the regular price X minus 0.16 X, which means taking the 16% discount of the whole price will be equal to the $756 that they told us. So now all we have to do is solve for X. So on the left hand side, we can factor out an X and we'll have that X multiplied by open parentheses. One minus 0.16, closed parentheses is equal to 756. And now we can divide by that parentheses. So we'll have that X is equal to divided by one minus 0.16. And now it's just a matter of simplifying. So we'll have that X is equal to 756 divided by and one minus 0.16 is 0.84. So now we're left with X is equal to 756 divided by 0.84 which when we plug that into our calculator, we'll have that X is equal to $900. And that'll be the price of the regular price of 10 technical handbooks or answer choice B in this case. So I hope that was helpful. And until next time.

After a 20% reduction, a 42-inch HDTV sold for $256. What was the price before the reduction?

Key Concepts

Percentage Reduction

Setting Up Equations

Solving Linear Equations

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