Question

1.A local bank has a debit card that gives a $3 reward each month you use your card for $50 or more in purchaces. Write an equation relating rewards earned,y, to total monthly purchaces, x. Give the domain of this function.
2. A local credit union has a debit card that rewards 3% of your total monthly purchases. Write an equation relating rewards earned,y, to total monthly purchases, x. Give domain of this function.

Answer 1

the second one is easiest i think
you get 3% of your monthly purchases, so if you call your monthly purchases \(x\) then you get \(y=0.03x\)

Answer 2

it has no lower limit, so i would say the domain is \((0,\infty)\) or "positive numbers"

Answer 3

Honestly, any input would be appreciated. I'm totally clueless!

Answer 4

this is not quite accurate, since you cannot spend say \(\pi\) dollars so maybe the domain is positive integers

Answer 5

how fancy is this math class?

Answer 6

maybe you can get away with saying "positive numbers"

Answer 7

It's just Algebra 1

Answer 8

okay so you probably don't have to be so picky
for the second one you can use \(y=0.03x\) and say the domain is positive numbers

Answer 9

for the first one, it is really
\[y= \left\{\begin{array}{rcc}
0 & \text{if} & x <50\\
3& \text{if} & x \geq50
\end{array}
\right.
\]

Answer 10

but that might be too fancy as well, so maybe you can just say \(y=3\) if \(x\geq50\) or maybe even just say \(y=3\) and the domain is \(x\geq 50\)

Answer 11

Okay, thank you so much!! I've been stuck on math problems all night. I still have 3 more to go :(

Answer 12

are they hard?

Answer 13

go ahead and post, i will look,
or just ask here

Answer 14

I'll type it here, if that's alright

Answer 15

go ahead, i will answer if i can

Answer 16

1. Abigail orders a large 2 topping pizza for $14 and a medium 1 topping pizza for $10. If all coats of a medium pizza are 80% of a similar large pizza, find rhe price of a large plain cheese and the cost of each large pizza topping.

Answer 17

costs*

Answer 18

whoa this is going to take a second
not too long though

Answer 19

You don't have to do it if you don't want to! I understand.

Answer 20

oh no we can definitely do this for sure

Answer 21

Alrighty, thank you so much.

Answer 22

we can call the price of the topping \(y\) and the price of the large plain pizza \(x\) so the price of the medium plain pizza is \(0.8x\)

Answer 23

Okay

Answer 24

then the first part tells you
\[x+2y=14\] and the second part say
\[.8x+y=10\]

Answer 25

Right

Answer 26

now before we solve this, i can make a good guess, which is that \(x=10\) and \(y=2\)

Answer 27

because \(10+2\times 2=14\) and \(0.8x\times 10+2=8+2=10\)

Answer 28

i am assuming of course that the toppings for the large and small pizza are the same
if they are not the same you cannot solve the problem

Answer 29

Yeah

Answer 30

in any case to solve
\[x+2y=14\]\[.8x+y=10\] multiply the second equation by -2 and add
you get
\[x+2y=14\]
\[-1.6x-2y=-20\]
\[-.6x=-6\]
\[x=-6\div -.6=60\div 6=10\]

Answer 31

so it is right
large pizza is $10, medium is $8, toppings are $2

Answer 32

so far so good?

Answer 33

Thank you so much! You make the problems seem so much easier. I might actually get some sleep tonight for school tomorrow!

Answer 34

yw
any more or are you done?

Answer 35

I have one more.

Answer 36

It's the hardest one

Answer 37

k

Answer 38

ready?

Answer 39

Nathan wants to go to a hockey game with friends. Tickets are $18, but students can get discounted tickets for $12. They want to spend no more than $80, including $8 for parking. The vehicle they will take can only hold 7 people. Write and graph (it's a regualr coordinate graph) a system of foir inequalities modeling their possible ticket purchases. Let x= number of student tickets and y= number of regular tickets

Answer 40

one thing we know is that \(x+y\leq 7\)

Answer 41

because at most 7 people can go

Answer 42

we also know that they are going to pay $8 for parking, leaving \(80-8=\$72\) for tickets and so \(12x+18y\leq 72\)

Answer 43

i think the other two inequalities are the easy ones, both \(x\geq 0\) and \(y\geq 0\) which just means you are in quadrant 1

Answer 44

can you graph \(x+y=7\)?

Answer 45

Uh, no :/

Answer 46

if \(x=0\) you get \(y=7\) so \((0,7)\) is on the graph, and similarly \((7,0)\) is on the graph
plot the points, connect the dots

Answer 47

you got it from the picture?

Answer 48

I can't see your drawing because I'm on my phone, I can't access a computer.

Answer 49

I know how to graph points, so I should be fine

Answer 50

ooh ok

Answer 51

Whatt do I do next?

Answer 52

the line \(12x+18y=72\) contains the points \((0,4)\) and \((6,0)\) so plot those points as well and connect the dots

Answer 53

then shade everything in quadrant 1, and below those two lines

Answer 54

i obviously cannot draw it here for you to see, but that is what you have to do

Answer 55

Yes, I understand

Answer 56

then i guess you are done
any point that is shaded in the picture is possible

Answer 57

Ok, sweet. Thank you very much for all your time and help. Have a nice night! :)

Answer 58

you too