7$ off and i get 10% off??

Question

you have a coupon good for $7 off the price of any large pizza. You also get 10% discount on any pizza if you show your student ID. How much more would you pay for a large pizza if the cashier applies the coupon first?

Answer 1

x=price of pizza

10% discount means you pay only 90%

coupon first, then take 90% of the lesser price after $7 coupon is deducted

0.9(x-7)=0.9x-6.3 is the price

discount first, then coupon

0.9x-7 is the price

compare 0.9x-7 and 0.9x-6.3

0.9x-7 is less than 0.9x-6.3

with coupon first you pay $0.70 more

you are taking $7 off of 90% of the original price by taking discount first as compared to taking $6.30 off of 90% of the original price if the coupon is applied first

example:

let a large pizza cost $20 for example

20-7=13, 13-1.3=$11.70

20-2=18, 18-7=$11.00

Answer 2

We need to compare what the price will be when we apply the coupon first to the price when we apply the discount first.

Let P=price of the pizza

C=cost to pay after coupon and discount

*Applying the 10% coupon means that we will actually pay only 90% of what it would normally cost.

APPLY COUPON FIRST

C=.9P-7 apply the coupon first then subtract the $7 student discount

APPLY DISCOUNT FIRST

C=(P-7) X .9 apply discount first then apply 10% coupon

C=.9P-6.3

As you can see you will actually pay $0.70 more if you apply the discount first because you will get $7 off the price with the coupon first as compared to getting only $6.30 with getting the discount first.