At this rate, how many dresses does Lucy sew in one hour?

"Lucy is a dress maker. She sew [tex]\frac{4}{7}[/tex] of a dress in [tex]\frac{3}{4}[/tex] hour. At this rate, how many dresses does Lucy sew in one hour?"

Let "x" represents the number of dresses that Lucy sews in one hour.

You need to analize the information given in the exercise.

According to the exercise, you know that, in [tex]\frac{3}{4}[/tex] hour, Lucy sews [tex]\frac{4}{7}[/tex] of a dress.

Then, knowing this data, you can set up the following proportion:

[tex]\frac{\frac{4}{7}}{\frac{3}{4}}=\frac{x}{1}[/tex]

Therefore, you must solve for "x" in order to find the he number of dresses that Lucy sew in one hour.

You get this result:

[tex](1)(\frac{4*4}{7*4})=x\\\\x=(1)(\frac{16}{21})\\\\x=\frac{16}{21}[/tex]

Then, Lucy sews [tex]\frac{16}{21}[/tex] of a dress in one hour.