Lucy is a dress maker. She sews 4 7 7 4 start fraction, 4, divided by, 7, end fraction of a dress in 3 4 4 3 start fraction, 3, divided by, 4, end fraction hour. Lucy sews at a constant rate. At this rate, how many dresses does Lucy sew in one hour? Include fractions of dresses if applicable.

of a dress

Step-by-step explanation:

For illustration

If in 3 hours, I sew 6 clothes

In 1 hour, I would sew (6/3) clothes.

Using the same analogy:

In hours, Lucy sews of a dress.

In 1 hour, Lucy will sew dresses

To simplify , We change the division sign to multiplication by taking the inverse of  the fraction after the division sign.i.e.

In 1 hour, Lucy sews of a dress.

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