percent savings problem

Question

Your tires needs new tires, and the dealer will install them for $785. Since you booked in advance, they took 10% off at the time of booking. You then found a coupon in the paper that will take 5% off at the register. Since they were special tires, there is a 5% rebate once you mail in the receipt. Does this result in a 20% total reduction? Find the total amount you paid using percent savings at each step and using a 20% savings all at once. How do they compare? If the percent savings is not 20%, what is the actual percent savings in this case?

Answer 1

MinHee,

 

I think it would go something like this:

 

$785 - 10% = $706.50          (by virtue of the advanced booking)

 

$706.50 - 5% = $671.18       (because of the coupon)

 

$671.18 - 5% = $637.62        (mail in rebate)

 

Now, if we start with the original price and deduct 20% from it we get

 

$785 - 20% = ($785)*(1 - 0.2) =  ($785)*(0.8) = $628

 

Difference =  $637.62 - $628 = $9.62

 

Finally, to calculate your true savings (expressed as a percentage of the original price)

 

$637.62 = what percent of $785?

 

If X is the unknown percentage

 

X = ($637.62)/($785) = 0.8123 or 81.23%

 

Your savings = 100% - 81.23% = 18.77%

Answer 2

To William's answer I would comment:

 

Mathematically,

 

this, "$785 - 10% = $706.50",

 

should be written, "$785 - 10%*$785 = $706.50",

 

or, "$785*(1 - 10%) = $706.50"

Answer 3

Take this question in parts.

 

The initial price was 785, but they took of the 10% for booking. So the new price is 785*.1=78.50->785-78.50=706.50

 

So when you go in to pay at the register WITHOUT the coupon, they charge you $706.50.

 

You tell them you have a coupon for 5% off. So now they do 5% of 706.50--->706.50*.05=35.33->706.50-35.33=671.17

 

At the register you'll pay $671.17, but after you send the receipt for the last 5% you'll have played a total of--->671.17*.05=33.56->671.17-33.56=637.61

 

So your total savings from the 10% for booking, 5% coupon, and the 5% rebate was 785-637.61=$147.39

 

If you'd used 20% all at once, this is what you'd have done:
785*.2=157, so the final cost would be 785-157=$628.

 

You would have been better if you could use the full 20% off at one time rather than doing all the individual discounts.

 

Hope this helps.

Answer 4

The initial price of the item was $785 dollars. At the time of the booking they took 10% off. That means that if you multiply (0.10) and (785) that will give you the ten percent discount. That initial discount is of $78.50.

 

Subtract it from the initial price. $785 - $78.50 = $706.50

 

Then from those $706.50 you took away 5% with the coupon. That means you have to multiply (0.05) and(706.50)= 35.325  

 

Subtract that from $706.50. So, $706.50 - 35.325 = $671.175

 

After that you got a final 5% discount by mail and rebate. Again multiply (0.05) and (671.175). That will give you 33.56.

 

Subtract it from $671.175. So, $671.175 - $33.56 = $637.62. THAT IS YOUR FINAL PRICE.

 

NOW, they ask you if that price is equal to a 20% reduction. Because if you take (0.20) times the initial price which is $785 that will give you $157 dollar discount. $785 - $157 = $628 which is a lower price than the one you actually got.

 

You get a better price if you discount the 20% complete from the very initial price.

 

The ACTUAL PERCENT SAVED  can be calculate by subtracting $637.62 - $785 = -147.38

 

Then you divide -147.38 by 785 and that give you -0.1877. That answer is in decimal. Multiply it by 100 and you get it in percent. The actual percent discount was 18.77%

 

The reason the final percent gave you negative was because you are calculating PERCENT DECREASE. Because it is a discount.

 

Good Luck and I hope this helped you in this question.