A math test is worth 100 points and has 30 problems. Each problem is worth either 3 or 4 points. Let "x" represent the number of 3-point problems and "y" represent the number of 4-point problems. now that you know that, i need an equation that would show the total possible points, and another equation showing the total number of problems.

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

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