Cups are sold by 6 per package while plates are sold by 8 per package. If you want to have the same number of each item for a party, what is the least number of
packages of cach item you need to buy?
A. 2 packages of cups and 3 packages of plates
3 packages of cups and 4 packages of plates
C. 4 packages of cups and 3 packages of plates
D. 5 packages of cups and 3 packages of plates
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C: 4 packages of cups and 3 packages of plates.

Step-by-step explanation:

Well let's work out A first. can be simplified to , but that isn't true, so A is false. B is next. can be simplified to , but that isn't true, so B is false. Let's solve C next.   can be simplified to , but that isn't true, so C is true! Let's work out D anyways, just to be sure the answer is C. can be simplified to , but that isn't true, so D is false, confirming that the answer is C.

Hope this helps!

sorry man i accidentally pressed yes my bad

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb