math help!?

Question

A store is having a "30% off everything" sale. The clerk adds up the cost of all your items and then takes 30% off its total. Do you get the same discount as if the clerk took 30% off each individual item and then totaled? Explain.

Answer 1

Basically you are asking if the following two equations are equivalent:

0.30(a + b + c + d + ... + z)
0.30a + 0.30b + 0.30c + 0.30d + ... + 0.30z

I hope you can see by the distributive property that the results will be exactly the same (discounting any rounding).

As a test, let's take 3 items for $5, $10, $20.

Added together you have $35. 30% is $10.50. The discounted total is $24.50

Done individually you have:
$5 --> 30% = $1.50 --> $3.50
$10 --> 30% = $3 --> $7.00
$20 --> 30% = $6 --> $14.00
Adding up you get $24.50

So as expected, the totals come out the same.

Answer 2

I assume this is a homework question, so I hope you'll take time to understand the concept here. Because of the distributive property, the answer is yes, the totals will be identical. This can be illustrated as follows:

let any 5 items be a, b, c, d, and e... so the question is:

is 0.7a + 0.7b + 0.7c + 0.7d + 0.7e equal to 0.7(a + b + c + d + e)

(0.7 = 70%, or what remains after 30% is taken off)

As you can see, if you distribute 0.7(a + b + c + d + e) you get 0.7a + 0.7b + 0.7c + 0.7d + 0.7e

Hope this helps :)

Answer 3

I'm not sure, I dont have a calulater....! But, i think it would be the same...Because if you had a total cost of 10 dollars 50% off would be 5 dollars. However, if you bought things, 1 worth 6 dollars and another thing worth 4dollars .......The 6 dollar would be 3 and the 4 dollar would be2 . And so 2+3=5!
Hope i helped!

Answer 4

Yes, with possible minor rounding error, because the price is rounded to the nearest cent. Also, taxes are applied individually rather than to all the items as a whole. That could also result in rounding differences.

Answer 5

let a,b,c,...be the costs of each kind of goods
the total cost after taking 30% : (a + b + c +....) * 30%
the total cost after taking 30% of every goods : a*30% + b*30% + c*30% + ...... = (a + b + c + .....) * 30%

Answer 6

Yes. The clerk is taking 30 percent off the sum of the entire purchase.

Whether you take 30% off of 10 dollars and end up with 7 dollars

or

take 30% off of 10 one dollar items
1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 + 1-0.3 = 7
($0.70 + $0.70 + $0.70 + $0.70 + $0.70 + $0.70 + $0.70 + $0.70 + $0.70 + $0.70 = $7.00)

You will still end up with the same discount.

Answer 7

Yes. Lets say you bought items costing x, y, & z
he is charging you .7(x+y+z) distributing the .7 gives .7x+.7y+.7z

If he calculates the discount individually he charges
.7x =.7y+.7z

same thing.

Answer 8

Are you just typing in all of your homework questions?!

It's the same. Example....
30%(2.00 + 1.00) = 30%(2.00) + 30%(1.00)

There's a property that proves that but I can't remember it's name...commutative?

Answer 9

Yes!!

Answer 10

do your own homework. how are you suppost to learn anything?