Sam went to tv city to buy a new tv. when he got there, he found that the manager was offering a 25% discount on every tv in the store. the one sam wanted was last year's model so he got an additional 10% discount on his purchase. when he got to the cash register, he found out he would save even more because the store offered a 5% discount for paying cash. these discounts were applies successively, and he paid $371.93 for the tv. what was the original price before any discounts were taken? what was the total percent discount sam got?

To express percentages in decimal form, you start with the decimal on the right side of the percentage, then you bring the decimal two places to the left. So for example, for 5%, it is 5. . When you bring the decimal two places to the left, it becomes .05 . 

We start with $371.93, then we multiply each percentage successively to this number. 

We work backwards. 

So we start with 5%. 

$371.93 = .95 x X 
X = $391.51 

Then we take X and do the same process for 10%. 

$391.51 = .90 x Y 
Y = $435.01 

Again, we take Y and do the same process for 25%. 

$435.01 = .75 x Z 
Z = $580.01 

So the original price is $580.01. 

To find the total percent discount, you take the total discounted price ($371.93) divided by the original price ($580.01). Then you have 1 subtracted by that number. Finally, you multiply the number by 100 to change it to a percentage. 

So its $371.93 / $580.01 which = .64125 

1 - .64125 = .35875 x 100 = 35.88% 

So your total percent discount is 35.88% 

31 is prime. and it’s prime factorization is just 31.