Question

A television repair store was offering a 5% discount on parts and a 5% discount on labor. An employee placed a sign in the store window that read “Receive 10% off of your total costs.” Use properties of real numbers to explain whether the sign was correct.

Answer 1

Let x be the price of repairs and y be the price of labor:
\[(x-0.05x)+(y-0.05y) \neq 0.10(x+y)\]

Answer 2

check with numbers

Answer 3

I just noticed that the above should have been:\[(x-0.05x)+(y-0.05y) \neq (x+y)- 0.10(x+y)\]

Answer 4

$100 parts
$200 labor
total cost $300

discount on parts, $5 you pay $95
discount on labor $10 you pay $190 for a total of $285

is this 10% off of $300 ?

Answer 5

I almost went that way with it too...best seen by example :)

Answer 6

Another (simpler) way to look at it would be:
\[0.95x+0.95y \neq 0.9(x+y)\]