Question

d. If you got your 60% discount and opened up the card for an additional 20%, what is the actual % discount you would receive?

Answer 1

Answer:

The actual discount is a 68% discount.

Step-by-step explanation:

Remember that if something has a price P, and you have a discount of the X%, the new price will be:

P' = P - P*(X%/100%) = P*(1 - X%/100%)

Here we first have a 60% discount, then if the initial price is P, the new price is:

P' = P*(1 - 60%/100%) = P*(1 - 0.6)

Now we have an additional 20% discount (this applies to the new price)

then the final price is:

P'' = P'*(1 - 20%/100%) = P'*(1 - 0.2) = P*(1 - 0.6)*(1 - 0.2)

We want to rewrite this as something like:

P'' = P*(1 - k)

Let's do this:

P'' = P*(1 - 0.6)*(1 - 0.2) = P*(1 - 0.2 - 0.6 + 0.2*0.6)

                                     = P*(1 - 0.8 + 0.12) = P*(1 - 0.68)

And this can be as:

P'' = P*(1 - 68%/100%)

Then the actual discount is a 68% discount.