The lenten on a map states that 1 inch is 40 miles. If you measure 5 inches on the map, how many miles would the actual distance be?

Work Shown:

(1 inch)/(40 miles) = (5 inches)/(x miles)

1/40 = 5/x

1*x = 40*5 cross multiply

x = 200 miles

We could also look at it like this:

1 inch = 40 miles

5*(1 inch) = 5*(40 miles) multiply both sides by 5

5 inches = 200 miles

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