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$Lucy is a dress maker. She sews (4)/(7) of a dress in (3)/(4) hour. Lucy sews at a constant rate. At this rate, how many dresses does Lucy sew in one hour? Include fractions of dresses if applicable. dresses$

Lucy is a dress maker. She sews $\frac{4}{7}$ of a dress in $\frac{3}{4}$ hour. Lucy sews at a constant rate. $\newline$ At this rate, how many dresses does Lucy sew in one hour? Include fractions of dresses if applicable. $\newline$ dresses

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Algebra 1

Interpret parts of quadratic expressions: word problems

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Q. Lucy is a dress maker. She sews

\frac{4}{7}

of a dress in

\frac{3}{4}

hour. Lucy sews at a constant rate.

\newline

At this rate, how many dresses does Lucy sew in one hour? Include fractions of dresses if applicable.

\newline

dresses

Set up proportion: Lucy sews $\frac{4}{7}$ of a dress in $\frac{3}{4}$ of an hour. To find out how many dresses she sews in one hour, we need to set up a proportion where the number of dresses is directly proportional to the number of hours. We can write this as $\frac{\frac{4}{7} \text{ dresses}}{\frac{3}{4} \text{ hour}} = \frac{x \text{ dresses}}{1 \text{ hour}}$ .
Isolate $x$ : To solve for $x$ , we multiply both sides of the equation by $1$ hour to isolate $x$ on one side. This gives us $x = \frac{4}{7} \text{ dresses} / \frac{3}{4} \text{ hour} \times 1 \text{ hour}$ .
Simplify equation: We simplify the right side of the equation by multiplying $(\frac{4}{7})$ by the reciprocal of $(\frac{3}{4})$ , which is $(\frac{4}{3})$ . This gives us $x = (\frac{4}{7}) \times (\frac{4}{3})$ dresses.
Multiply numerators and denominators: Now we multiply the numerators together and the denominators together. This gives us $x = (4 \times 4) / (7 \times 3)$ dresses.
Calculate final result: Calculating the multiplication, we get $x = \frac{16}{21}$ dresses. This is the number of dresses Lucy sews in one hour.