What a steal of a Deal!
Hunter 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 Hunter wanted was last year's model so he got an additional 10% discount on his purchase. When he got to the cash, he found out he would save even more because the store offered a 5% discount for paying cash. The discounts were applied successivelky, and he paid $371.93 for the TV. What was the original price before any discounts were taken? What was the total percent discount Hunter got?
original price = p
store discount = .25, so price was then .75p
obsolete discount = .1, so the price is now
.75p*.90 = .675p
cash discount is 5% so final price is
.675p*.95 = .64125p
total discount was 1.00 - .64 = 36%
.64125p = 371.93
p = $580.00
To find the original price before any discounts were taken, we can work backward from the final price.
Let's denote the original price as "P."
First, Hunter received a 25% discount on the TV. This means he paid 75% of the original price. So, after this discount, the price becomes 0.75P.
Next, he received an additional 10% discount on the discounted price. This means he paid 90% of the price after the first discount. So, after this second discount, the price becomes 0.9 * 0.75P = 0.675P.
Finally, he received a 5% cash discount on this second discounted price. This means he paid 95% of the price after the second discount. So, after this third and final discount, the price becomes 0.95 * 0.675P = 0.64125P.
We know that Hunter paid $371.93 for the TV, which is equal to 0.64125P. We can set up the equation:
0.64125P = $371.93
To solve for P, we divide both sides by 0.64125:
P = $371.93 / 0.64125
By calculating this, the original price before any discounts were taken is approximately $579.
To find the total percent discount Hunter got, we can calculate the difference between the original price and the final price (after all discounts) and express it as a percentage of the original price. The total percent discount is given by:
Total percent discount = ((Original price - Final price) / Original price) * 100
Before the final price, Hunter got three discounts: 25%, 10%, and 5%. Thus, the total percent discount is:
Total percent discount = (1 - (Final price / Original price)) * 100 = (1 - ($371.93 / $579)) * 100
By calculating this, the total percent discount Hunter got is approximately 35.8%.