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.

- anonymous

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- anonymous

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 \(y=0.03x\)

- anonymous

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

- anonymous

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

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## More answers

- anonymous

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

- anonymous

how fancy is this math class?

- anonymous

maybe you can get away with saying "positive numbers"

- anonymous

It's just Algebra 1

- anonymous

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

- anonymous

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

- anonymous

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 \(x\geq 50\)

- anonymous

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

- anonymous

are they hard?

- anonymous

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

- anonymous

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

- anonymous

go ahead, i will answer if i can

- anonymous

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.

- anonymous

costs*

- anonymous

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

- anonymous

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

- anonymous

oh no we can definitely do this for sure

- anonymous

Alrighty, thank you so much.

- anonymous

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 \(0.8x\)

- anonymous

Okay

- anonymous

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

- anonymous

Right

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Yeah

- anonymous

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

- anonymous

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

- anonymous

so far so good?

- anonymous

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

- anonymous

yw
any more or are you done?

- anonymous

I have one more.

- anonymous

It's the hardest one

- anonymous

k

- anonymous

ready?

- anonymous

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

- anonymous

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

- anonymous

because at most 7 people can go

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Uh, no :/

- anonymous

|dw:1363921714846:dw|

- anonymous

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

- anonymous

you got it from the picture?

- anonymous

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

- anonymous

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

- anonymous

ooh ok

- anonymous

Whatt do I do next?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Yes, I understand

- anonymous

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

- anonymous

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

- anonymous

you too

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