Tomas makes balloon sculptures at a circus. in 180 minutes, he uses 252 minutes to make 36 identical balloon sculptures.
b) what is tomas’s unit rate for balloons used per minute?
explanation would be appreciated : )

Tomas makes balloon sculptures at a circus.in 180 minutes,he uses 252 balloons to make 36 identical balloon sculptures.

b. what is tomas's unit rate for balloons used per minute.

Tomas unit rate for ballons used per minute is 1.4 ballons per minute

Given that in 180 minutes, tomas uses 252 ballons to make 36 identical sculptures

To find number of minutes to make 1 sculpture divide 180 by 36

So he takes 5 minutes to make 1 sculpture

Given that he uses 252 ballons to make 36 sculptures

To find number of ballons in 1 sculpture divide 252 by 36

So he uses 7 ballons in 5 minutes

To find unit rate for ballons used per minute divide 7 by 5

Thus tomas unit rate for ballons used per minute is 1.4 ballons per minute

hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)