Terry runs a snowplowing business. Income from snowplowing is given by the function f(x) = 35.5x + 6, where f(x) is the income in dollars and x is the snowfall in inches received during a winter. If during the years 2006 to 2011, Terry’s town received 53, 42, 55, 63, 58, and 47 inches of snowfall, what was his income (in dollars) during those years?

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

6 cars because if you have 8 and subtract 2 youll have 6 left over

set the two equations for y equal to each other. solve for x. this will be the x-coordinate for the point of intersection. use this x-coordinate and plug it into either of the original equations for the lines and solve for y.