SOLUTION: Your local electronices store is having an end of the year sale. The price on a large screen tv had been reduced by 30%. Now the sale price is reduced by another 30%. If x is the t

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 289569: Your local electronices store is having an end of the year sale. The price on a large screen tv had been reduced by 30%. Now the sale price is reduced by another 30%. If x is the tv's original price the sale price can be represented by (x-0.3x)-0.3(x-0.3x)
a. Factor out (x-0.3x) from each term. Then simplify the resulting expression
b. Use the simplified expression from part a to answer these questions. With a 30% reduction followed by a 30% reduction is the tv selling at 40% of the original price? If not a what percentage of the original price is it selling?

I cant for the life of me figure these 2 problems out.. HELP!!!!
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
a) First note that x-0.3x=x(1-0.3)=x(0.7)=0.7x or in other words, x-0.3x=0.7x

So the complicated expression (x-0.3x)-0.3(x-0.3x) simplifies to 0.7x-0.3(0.7x). Multiply 0.3 and 0.7 to get 0.21. So we should now have 0.7x-0.21x

Now factor out the GCF 'x' to get x(0.7-0.21) and subtract to get x(0.49)=0.49x

So (x-0.3x)-0.3(x-0.3x) = 0.49x

b) Because 'x' is the original price, this means that 0.49x is the sale price after the discounts. We can think of 0.49 as 1-z=0.49 where 'z' is some unknown percent discount. Solve for 'z' to get z=1-0.49=0.51

So x-0.51x=0.49x which means that we subtracted off 51% of the original price 'x' to get the new sale price 0.49x

So a 30% price reduction followed by another 30% price reduction yields a total of a 51% discount.