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Drake and Cleo are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit 28 students in a 756 square foot area. Assuming that each student has a spot x feet wide and 3 times as long, what is the length, in feet, of the space they are allotting to each student? Choose 1 answer: (A) 1 feet (B) 3 feet (c) 9 feet (D) 27 feet

Drake and Cleo \mathrm{Cleo} are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit 2828 students in a 756756 square foot area. Assuming that each student has a spot x x feet wide and 33 times as long, what is the length, in feet, of the space they are allotting to each student?\newlineChoose 11 answer:\newline(A) 11 feet\newline(B) 33 feet\newline(C) 99 feet\newline(D) 2727 feet

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Q. Drake and Cleo \mathrm{Cleo} are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit 2828 students in a 756756 square foot area. Assuming that each student has a spot x x feet wide and 33 times as long, what is the length, in feet, of the space they are allotting to each student?\newlineChoose 11 answer:\newline(A) 11 feet\newline(B) 33 feet\newline(C) 99 feet\newline(D) 2727 feet
  1. Understand the problem: Understand the problem.\newlineWe need to find the length of the space for each student, given that the total area is 756756 square feet and it fits 2828 students. Each student's space is xx feet wide and 33 times as long.
  2. Calculate area per student: Calculate the area for each student.\newlineSince the total area is 756756 square feet and there are 2828 students, we divide the total area by the number of students to find the area per student.\newlineArea per student = Total areaNumber of students\frac{\text{Total area}}{\text{Number of students}}\newlineArea per student = 756 square feet28 students\frac{756 \text{ square feet}}{28 \text{ students}}
  3. Perform division: Perform the division to find the area per student.\newlineArea per student = 75628\frac{756}{28}\newlineArea per student = 2727 square feet
  4. Set up equation: Set up the equation for the area of each student's space.\newlineWe know that the width is xx feet and the length is 33 times the width. So, the area of each student's space is x×(3x)x \times (3x).\newlineArea per student = x×(3x)x \times (3x)\newline2727 square feet = x×(3x)x \times (3x)
  5. Solve for x: Solve for x.\newlineTo find xx, we need to solve the equation 27=3x227 = 3x^2.\newlineDivide both sides by 33 to simplify the equation.\newline273=3x23\frac{27}{3} = \frac{3x^2}{3}\newline9=x29 = x^2
  6. Find value of x: To find xx, we take the square root of both sides.\newlinex=9x = \sqrt{9}\newlinex=3x = 3 feet
  7. Determine length: Determine the length of each student's space.\newlineSince the length is 33 times the width, we multiply xx by 33.\newlineLength =3×x= 3 \times x\newlineLength =3×3= 3 \times 3 feet\newlineLength =9= 9 feet

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