## calculusxy one year ago In a certain coffee shop, a large latte costs 2 dollars more than a medium latte, and a medium latte costs 2 dollars more than a small latte. If 12 small lattes cost 2x dollars, how much will 5 large and 7 medium lattes cost? A. 2x + 24 B. 2x + 34 C. 2x + 48 D. 12x + 24 E. 24x + 3

1. calculusxy

@jim_thompson5910

2. jim_thompson5910

what does x represent?

3. calculusxy

I don't know. That is confusing me.

4. jim_thompson5910

cost of large latte? medium? or small?

5. calculusxy

Can we assume that x=6?

6. jim_thompson5910

where are you getting that?

7. calculusxy

nvm

8. jim_thompson5910

S = cost of small M = cost of medium L = cost of large

9. jim_thompson5910

a large latte costs 2 dollars more than a medium latte so L = M+2 agreed?

10. calculusxy

yes

11. jim_thompson5910

 medium latte costs 2 dollars more than a small latte using the variables I set up, what equation do you get?

12. calculusxy

S = x M = x + 2 L = 2 + (x + 2) or 4 + x

13. jim_thompson5910

S = unknown (not x) M = S + 2 L = M + 2 = (S+2) + 2 = S + 4 12 small lattes cost 2x dollars 12S = 2x S = (2x)/(12) S = x/6 how much will 5 large and 7 medium lattes cost? 5L + 7M = 5(S+4) + 7(S+2)

14. jim_thompson5910

the next step is to plug S = x/6 into 5(S+4) + 7(S+2)

15. calculusxy

so we are learning about plugging in numbers. can we work around that level?

16. jim_thompson5910

you mean replacing S with some number like 7?

17. calculusxy

yeah

18. jim_thompson5910

how would you get to the answer? each answer has an x in it

19. calculusxy

so can we like plug in 7 for x?

20. calculusxy

I am really confused on this.

21. jim_thompson5910

Do you see how I got 5(S+4) + 7(S+2) ?

22. calculusxy

yes

23. jim_thompson5910

$\Large 5(S+4) + 7(S+2) = 5(\frac{x}{6}+4) + 7(\frac{x}{6}+2)$ $\Large 5(S+4) + 7(S+2) = 5(\frac{x}{6})+5(4) + 7(\frac{x}{6})+7(2)$ $\Large 5(S+4) + 7(S+2) = \frac{5x}{6}+20 + \frac{7x}{6}+14$ I'll let you simplify

24. calculusxy

12x/6 + 34

25. jim_thompson5910

12x/6 simplifies to ???

26. calculusxy

2x

27. calculusxy

THANK YOU!!!

28. jim_thompson5910

29. jim_thompson5910

np

30. calculusxy

I have another question

31. calculusxy

If $a = 2x + 3$ and $b = 4d$ what is b in terms of a? A. $(a - 3)^2$ B.$2(a - 3)^2$ C. $\frac{ (a-3)^2 }{ 4 }$ D. $\frac{ (a + 3)^2 }{ 4 }$ E. $a + 3$

32. jim_thompson5910

b = 4d? is that a typo?

33. calculusxy

Yes sorry $b = 4d^2$

34. jim_thompson5910

and a = 2x + 3 is correct? or no?

35. calculusxy

that's correct

36. jim_thompson5910

I don't see how to connect a and b. They have no variables in common

37. calculusxy

i have checked with many numbers none of which seems to work

38. jim_thompson5910

something seems missing

39. calculusxy

i will check on that with my teacher. thank you :)

40. jim_thompson5910

np