Question

You have a coupon for your favorite clothing store for $25 off any purchase of more than $50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the $25 coupon applied, and g(x) be the price with the 20% discount applied.

a. Write an expression for f(x).

b. Write an expression for g(x).

c. What would the expression (f o g)(x) represent?

d. What would the expression (g o f)(x) represent?

e. If the store allows you to apply both the 20% discount and the $25-off coupon, does it matter which you apply first? How do y

Answer 1

***There are 5 parts.. :/ Can u please explain? Thank you :)

Answer 2

If something costs x dollars and you apply a $25 coupon, how much is it now?

Answer 3

x-25
??

Answer 4

exactly

Answer 5

so f(x) = x - 25

Answer 6

oh that simple? so that's my answer to part a?
f(x)= x-25
??

Answer 7

If something costs x dollars, and you apply a 25% discount, then the final price will become

x - 0.25x = 0.75x

So g(x) = 0.75x

Answer 8

ohhh i see... :) so now i apply that to part c??

Answer 9

(f o g)(x) = f(g(x))

Answer 10

so for part c i do this?
(f o g)(x)=f(g(x))
??? did i do that right?

Answer 11

oh wait lol nvm u just wrote that.. my bad! haha so i do this now?
f(g(x))=f(0.75x)
??

Answer 12

good, keep going

Answer 13

okay, so do i substitute f(x) now?

Answer 14

f(x) = x - 25

f(0.75x) = 0.75x - 25

is that what you meant?

Answer 15

yeah :) was that right?

Answer 16

now do the reverse for part d

Answer 17

wait so was this my answer for part c?
(f o g)(x)= 0.75x - 25
??

Answer 18

yes

Answer 19

okay :) so for part d i get this?
(g o f)(x)= g(f(x))
=g(x - 25)
and I'm confused about the next step... did i do the previous steps correctly?

Answer 20

you're doing great so far

Answer 21

okay, so i have this??
g(x-25)= -25 +0.75 x
??? idk i'm confused :(

Answer 22

g(x) = 0.75x

g(x-25) = 0.75(x - 25)

g(x-25) = 0.75x - 0.75*25

g(x-25) = 0.75x - 18.75


So g(f(x)) = 0.75x - 18.75

Answer 23

ohhh that makes sense now! so i write out part d like this then??
(g o f)(x)= 0.75x - 18.75
?? is that how i write the answer to part d?

Answer 24

yes it is

Answer 25

awesome! so i'm especially confused about part e... like how do i solve that? :O

Answer 26

So part c was

0.75x - 25

part d was

0.75x - 18.75

which one offers the better discount?

Answer 27

ohhh i use parts c and d to answer part e?

Answer 28

is part c the 20% discount? or is part d? and which one is the $25 dollar off coupon?

Answer 29

yes you compare parts c and d and see which one gives you the better discount

Answer 30

oh in that case, i think the $25 dollar discount is better right?? part c is the better discount?? since it is -25, which is more than -18.75?? am i right?

Answer 31

and am i right when i say that part c is the $25 off coupon and part d is the 20% off discount?

Answer 32

parts c and d are a mix of both

Answer 33

ohhh then how do i know which to apply first then? i'm lost now :(

Answer 34

(f o g)(x) means apply g first, then apply f

(g o f)(x) means apply f first, then apply g

Answer 35

it seems to me that part c is the best since you save 6.25 more... i think... ohhh so would it matter or not?

Answer 36

part c you are saving more, you got it

Answer 37

so applying the 25% coupon first, then taking off 25 dollars gives you the better discount

Answer 38

because of what i said?

Answer 39

yes

Answer 40

okay so can i phrase part e like this?
e. It does matter, because applying the 20% discount would save you 18.75 and then you could use the $25 off coupon to save $6.25 more than you would if you had used the $25 off coupon first and then used the 20% off discount. When your total is higher, you save more from the 20% off discount. In this case, by using the 20% discount first and then using the $25 off coupon, you would save $6.25 more than you would have if you had used them the other way around.

is that okay?

Answer 41

*and is that correct?? is that the correct answer for part e???? :/ :/

Answer 42

ugh, sry i misread above and it's not 25%...it's 20%....idk why i didn't catch that til now

Answer 43

something wasn't matching up and i know why now

Answer 44

oh okay, so is my answer incorrect??

Answer 45

the one i typed for my answer as e above, is it wrong then @jim_thompson5910 ? :O

Answer 46

yeah unfortunately it is

Answer 47

idk why I'm seeing this now, my bad

Answer 48

aww :( but i answered based off of 20% discount and $25 off :/

Answer 49

it's okay :)

Answer 50

so is answer b incorrect also?? and answers b,c, and d are incorrect then right??

Answer 51

Here's what everything should be

a)

f(x) = x - 25

-------------

b)

g(x) = 0.8x

-------------

c)

(f o g)(x) = 0.8x - 25

-------------

d)

(g o f)(x) = 0.8x - 20


-------------

part c) still gives you the better discount

Answer 52

okay so could u pls show me how you got b, c, and d?? like the steps?? i need to show work :/ and i also do not understand how u got those answers :/

Answer 53

If you apply a 20% discount, then you subtract off 20% of the original cost.

If the original price was x, then 20% of x is 0.2x

So the new price is x - 0.2x = 0.8x

Therefore, g(x) = 0.8x

Answer 54

oh i see,... but what about parts c and d?

Answer 55

f(x) = x - 25

f(g(x)) = g(x) - 25

f(g(x)) = 0.8x - 25

(f o g)(x) = 0.8x - 25

Answer 56

g(x) = 0.8x

g(f(x)) = 0.8(f(x))

g(f(x)) = 0.8(x-25)

g(f(x)) = 0.8x-0.8*25

g(f(x)) = 0.8x-20

(g o f)(x) = 0.8x-20

Answer 57

oh okay thanks!! so for part e it matters which i apply first right?

Answer 58

it does matter yes

Answer 59

okay, well i still think if i apply the 20% off (part d right?) coupon first, that's better, right? because i would save $5 more that way if i got 20% off first and then got $25 off right?? am i right? i would save $5 more?

Answer 60

no, part c) is where you apply the 20% coupon first

Answer 61

ohh i see... my bad! so applying the $25 off coupon first and then using the 20% discount would save you $5 more than if you used the $25 off coupon first? am i right?

Answer 62

no, applying the 20% discount first then the $25 discount will save you 5 more dollars

Answer 63

ohhh would that be using part c is the best choice? is that it?

Answer 64

yes part c) is the best option if you want to save the most money

Answer 65

okay so is this a good way to write my answer for part e? (lemme write it out)

Answer 66

e. It does matter, because applying the 20% discount first and then using the $25 off coupon would save you $5 more than if you were to use the $25 off coupon first and then use the 20% discount. When your original total is higher, you save more from a percentage discount than a dollar discount, therefore, it matters since you would save $5 more if you use the 20% discount before you apply the $25 off coupon.

Answer 67

does that look alright to you??

Answer 68

That looks correct

the last bit "When your original total is higher, you save more from a percentage discount than a dollar discount, therefore, it matters since you would save $5 more if you use the 20% discount before you apply the $25 off coupon." isn't 100% true

Basically, you save more with applying the percent discount first, then taking off $25 every time

Note: obviously the total must be above a certain mark for the discounts to apply (ie you're not going to have a discount that deducts the total price to $0 or below)

Answer 69

so just take that part out??

and this will be my answer?
e. It does matter, because applying the 20% discount first and then using the $25 off coupon would save you $5 more than if you were to use the $25 off coupon first and then use the 20% discount. Therefore, it matters which you apply first, because if you use the 20% discount first and then use the $25 off coupon, you will save $5 more.

***i fixed it a bit... does that look ok now? :)

Answer 70

looks much better

Answer 71

those are the final, correct answers??! :O

Answer 72

looks perfect

Answer 73

awesome!! THank you sooooo much!! :D

Answer 74

you're welcome