You are trying to ship a package to a friend in another state, UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first
pound, and $0.30 for each additional pound. How many pounds will it take for UPS
and FedEx to cost the same?
**Write an equation, using p for pounds, that represents this situation (first blank),
**Solve your equation (second blank),
**Finally, give the cost of sending that weight of package with either carrier (third
blank - do not include the dollar sign $ - I already have for you!).
An equation to represent this situation is
When a package is
pounds, it will cost $
for either carrier,

$7 + $0.20p = $5 + $0.30p

Step-by-step explanation:

UPS charges $7 for the first pound and $0.20 for each additional pound.

FedEx charges $5 for the first pound and $0.30 for each additional pound.

Let's take the number of  additional pounds that will make UPS and FedEx cost the same to be p.

$7 + $0.20p = $5 + $0.30p

$7 - $5 = $0.30p - $0.20p

$2 = $0.10p

p = = 20 additional pounds

tip $2.90

total $17.40

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)