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

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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

Mathematics
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what does x represent?
I don't know. That is confusing me.

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cost of large latte? medium? or small?
Can we assume that x=6?
where are you getting that?
nvm
S = cost of small M = cost of medium L = cost of large
`a large latte costs 2 dollars more than a medium latte` so L = M+2 agreed?
yes
` medium latte costs 2 dollars more than a small latte` using the variables I set up, what equation do you get?
S = x M = x + 2 L = 2 + (x + 2) or 4 + x
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)
the next step is to plug S = x/6 into 5(S+4) + 7(S+2)
so we are learning about plugging in numbers. can we work around that level?
you mean replacing S with some number like 7?
yeah
how would you get to the answer? each answer has an x in it
so can we like plug in 7 for x?
I am really confused on this.
Do you see how I got 5(S+4) + 7(S+2) ?
yes
\[\Large 5(S+4) + 7(S+2) = 5(\frac{x}{6}+4) + 7(\frac{x}{6}+2) \] \[\Large 5(S+4) + 7(S+2) = 5(\frac{x}{6})+5(4) + 7(\frac{x}{6})+7(2) \] \[\Large 5(S+4) + 7(S+2) = \frac{5x}{6}+20 + \frac{7x}{6}+14 \] I'll let you simplify
12x/6 + 34
12x/6 simplifies to ???
2x
THANK YOU!!!
so 2x+34 is the answer
np
I have another question
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. \[a + 3\]
b = 4d? is that a typo?
Yes sorry \[b = 4d^2\]
and a = 2x + 3 is correct? or no?
that's correct
I don't see how to connect a and b. They have no variables in common
i have checked with many numbers none of which seems to work
something seems missing
i will check on that with my teacher. thank you :)
np

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