Desiree and Nick, the boy she was babysitting, were playing basketball together. Her score was 20 points, and his score was 10 points. Desiree wanted to make the game more
fair, so she called a time-out and modified the rules a bit. Desiree explained that, for the
rest of the game, she would get 3 points per basket, and Nick would get 4 points per
basket. Then they played a bit longer. After the time-out, they both made the same
number of baskets and ended up with a tied score. How many baskets did each person
make after the time out?

step-by-step explanation:

ask goog great chance of finding the solution there

correct answer is b. 27/8

step-by-step explanation:

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)