Question 1:
tom wants to buy a sweater for $30. in which city will it be the least expensive? show your work, .

sales tax in cities

a. city a: 3%

b. city b: 4.1%

c. city c: 2.9%

question 2:
how much will tom's $30 sweater cost in city b?
a. $30.90
b. $31.23
c.$30.87

#1) A 3%

#2)B 31.23

Step-by-step explanation:

Sweater is least expensive in City C with 2.9% sales Tax

Cost of Sweater in city B is $31.23

Step-by-step explanation:

Cost of a sweater = $30

Sales tax in city A= 3%

Cost in City A = $30 + ($30*3%)

= $(30 +0.9)=$30.9

Sales tax in City B = 4.1%

Cost in City B = $30+($30*4.1%)

= $(30+1.23)=$31.23

sales tax in city C = 2.9%

Cost in City C = $30+($30*2.9%)

=$(30+0.87)=$30.87

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)