Question

Lucy is a dress maker. She sews 4/7 of a dress in 3/4 hour. At this rate, how many dresses does Lucy sew in one hour?

Answer 1

`16/21 " dresses"`

Explanation:

The ratio of time required to dresses made is
`color(white)("XXX")3/4* k " hours" : 4/7 * k " dresses"` for any constant `k`

Specifically, if we want `1 " hour"` then `k` will need to be `color(green)(4/3)`.

So `(color(red)(cancel(color(black)3)))/(color(blue)(cancel(color(black)4)))xx(color(blue)(cancel(color(green)4)))/(color(red)(cancel(color(green)3))) " hours" : 4/7 xx color(green)(4/3) " dresses"`

`rArr 1 " hour" : 16/21 "dresses"`