Question

Suppose you have a coupon for 10% off and you use it to buy a CD which was already discounted 15%. Do you end up with a discount of 25%? Explain your answer

Answer 1

There are two ways to apply a discount: in series (one after the other) and in parallel (at the same time).

To apply a discount in series, you have to multiply one after the other. Basically:
\[
D_1 = A - A\times 0.10 \quad D_2 = D_1 - D_1\times 0.15
\]discount in parallel, you just add them an multiply them:\[
D = A - A \times (0.10 + 0.15) = A - A \times 0.25
\]
The 25% they are getting makes since is the discount is done in parallel. However when they say "Already discounted" to me gives the impression that the discounts are applied in series rather than in parallel.

Answer 2

\[
D_1 = A \times (1-0.10) \\
D_2 = D_1 \times (1-0.15) = A\times (1-0.10) \times (1-0.15) \\
= A - A\times[1- (1-0.10) \times (1-0.15)]\\
= A - A\times(1- 0.90 \times 0.85)\\
= A - A \times (1 - 0.765) \\
= A - A \times 0.235
\]

Answer 3

So doing a discount in series should give you something like 23.5% effective discount from the original price. I hope it makes sense.

Answer 4

here is an easy way if the CD cost $10 originally then

15% is $1.50 so the marked price is $8.50

and then you get an extra 10% = $0.85

so you would pay $7.65

so your saving off the original price is $2.35

2.35/10 x 100 = 23.5%

25% discount of the price of $10 is $2.50

so by having 15% and then 10% you receive a lesser discount.

Answer 5

No. Let the orginal item cost be $10.
\[\left(\text{$\$$10}.00*\frac{85}{100}\right)*\frac{90}{100}=\text{$\$$7}.65 \]\[\left(\text{$\$$10}.00*\frac{75}{100}\right)=\text{$\$$7}.50 \]