A clothier who only makes shirts and pants can make a shirt in 4 hours and a pair of pants in 6 hours. Which of the following equations shows the number of shirts, s, and the number of pants, p, that the clothier can make in a 40 hour work week?

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Calculate Rates: Determine the rate at which the clothier can make shirts and pants. The clothier can make a shirt in 4 hours and a pair of pants in 6 hours. This means in one hour, the clothier can make 1/4 of a shirt and 1/6 of a pair of pants.Total Production in 40 Hours: Calculate the total number of shirts and pants that can be made in 40 hours. Since the clothier works for 40 hours, we multiply the hourly rate of making shirts and pants by 40 to find the total number of shirts and pants that can be made. For shirts: $ \frac{1}{4} \text{ shirt/hour} \times 40 \text{ hours} = 10 \text{ shirts} $ For pants: $ \frac{1}{6} \text{ pair of pants/hour} \times 40 \text{ hours} = \frac{40}{6} \text{ pairs of pants} $Equation for Shirts and Pants: Write the equation that represents the relationship between the number of shirts, s, and the number of pants, p, that the clothier can make in 40 hours. Let s be the number of shirts and p be the number of pants. The clothier's work for shirts and pants can be represented by the equations: $ s = \frac{1}{4} \times 40 $ $ p = \frac{1}{6} \times 40 $ However, these equations give us the exact number of shirts and pants, not a relationship between s and p. We need to find an equation that relates s and p to the total time worked, which is 40 hours.Combine Rates for Equation: Combine the rates to form a single equation. The total time spent making shirts and pants should add up to 40 hours. The time spent on shirts is 4 hours per shirt, and the time spent on pants is 6 hours per pair of pants. The equation is: $ 4s + 6p = 40 $ This equation shows the relationship between the number of shirts, s, and the number of pants, p, that the clothier can make in a 40-hour work week.

A clothier who only makes shirts and pants can make a shirt in $4$ hours and a pair of pants in $6$ hours. Which of the following equations shows the number of shirts, $s$ , and the number of pants, $p$ , that the clothier can make in a $40$ hour work week?

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A clothier who only makes shirts and pants can make a shirt in $4$ hours and a pair of pants in $6$ hours. Which of the following equations shows the number of shirts, $s$ , and the number of pants, $p$ , that the clothier can make in a $40$ hour work week?