Nina can stitch $\frac{2}{3}$ of a dress in 4 hours. If $d$ represents the number of dresses and $h$ represents the number of hours, which equation represents this proportional relationship?
A. $d=6 h$
B. $3 d=4 h$
C. $d=\frac{1}{6} h$
D. $d=4 h$
E. $\frac{1}{6} d=12 h
Answer (2)
Calculate the rate at which Nina stitches dresses: 4 2/3 = 6 1 .
Set up the equation representing the proportional relationship: d = 6 1 h .
Compare the equation with the given options.
The correct equation is: d = 6 1 h .
Explanation
Understanding the Problem We are given that Nina can stitch 3 2 of a dress in 4 hours. We need to find the equation that represents the proportional relationship between the number of dresses, d , and the number of hours, h .
Finding the Rate First, we need to find the rate at which Nina stitches dresses. We know that she stitches 3 2 of a dress in 4 hours. To find the number of dresses she stitches in 1 hour, we divide the number of dresses by the number of hours: 4 3 2 = 3 2 ÷ 4 = 3 2 × 4 1 = 12 2 = 6 1 So, Nina stitches 6 1 of a dress in 1 hour.
Setting up the Equation Now we can set up the equation that represents the proportional relationship between d and h . Since d represents the number of dresses and h represents the number of hours, and Nina stitches 6 1 of a dress in 1 hour, we can write the equation as: d = 6 1 h This equation tells us that the number of dresses Nina stitches is equal to 6 1 times the number of hours she works.
Comparing with the Options Now we compare our equation with the given options: A. d = 6 h B. 3 d = 4 h C. d = 6 1 h D. d = 4 h E. 6 1 d = 12 h Our equation d = 6 1 h matches option C.
Examples
Understanding proportional relationships is useful in many real-life situations. For example, if you are baking a cake and the recipe calls for 2 cups of flour for every 1 cup of sugar, you can use a proportional relationship to determine how much flour you need if you want to use 3 cups of sugar. Similarly, if you are traveling and know that you can drive 100 miles on 5 gallons of gas, you can use a proportional relationship to determine how far you can drive on 12 gallons of gas. These types of calculations are essential for everyday tasks and planning.
Nina stitches 3 2 of a dress in 4 hours, which means she stitches 6 1 of a dress in 1 hour. Therefore, the equation that represents the relationship between the number of dresses d and the hours h is d = 6 1 h , matching option C. The correct answer is C.
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