KaylaClemens15 2 years ago 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.

1. satellite73

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 $$y=0.03x$$

2. satellite73

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

3. KaylaClemens15

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

4. satellite73

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

5. satellite73

how fancy is this math class?

6. satellite73

maybe you can get away with saying "positive numbers"

7. KaylaClemens15

It's just Algebra 1

8. satellite73

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

9. satellite73

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

10. satellite73

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 $$x\geq 50$$

11. KaylaClemens15

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

12. satellite73

are they hard?

13. satellite73

14. KaylaClemens15

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

15. satellite73

16. KaylaClemens15

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.

17. KaylaClemens15

costs*

18. satellite73

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

19. KaylaClemens15

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

20. satellite73

oh no we can definitely do this for sure

21. KaylaClemens15

Alrighty, thank you so much.

22. satellite73

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 $$0.8x$$

23. KaylaClemens15

Okay

24. satellite73

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

25. KaylaClemens15

Right

26. satellite73

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

27. satellite73

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

28. satellite73

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

29. KaylaClemens15

Yeah

30. satellite73

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

31. satellite73

so it is right large pizza is $10, medium is$8, toppings are $2 32. satellite73 so far so good? 33. KaylaClemens15 Thank you so much! You make the problems seem so much easier. I might actually get some sleep tonight for school tomorrow! 34. satellite73 yw any more or are you done? 35. KaylaClemens15 I have one more. 36. KaylaClemens15 It's the hardest one 37. satellite73 k 38. satellite73 ready? 39. KaylaClemens15 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 40. satellite73 one thing we know is that $$x+y\leq 7$$ 41. satellite73 because at most 7 people can go 42. satellite73 we also know that they are going to pay$8 for parking, leaving $$80-8=\72$$ for tickets and so $$12x+18y\leq 72$$

43. satellite73

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

44. satellite73

can you graph $$x+y=7$$?

45. KaylaClemens15

Uh, no :/

46. satellite73

|dw:1363921714846:dw|

47. satellite73

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

48. satellite73

you got it from the picture?

49. KaylaClemens15

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

50. KaylaClemens15

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

51. satellite73

ooh ok

52. KaylaClemens15

Whatt do I do next?

53. satellite73

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

54. satellite73

55. satellite73

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

56. KaylaClemens15

Yes, I understand

57. satellite73

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

58. KaylaClemens15

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

59. satellite73

you too