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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 $\mathrm{Cleo}$ 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? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ feet $\newline$ (B) $3$ feet $\newline$ (C) $9$ feet $\newline$ (D) $27$ feet

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Scale drawings: word problems

Full solution

Q. Drake and

\mathrm{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?

\newline

Choose

1

answer:

\newline

(A)

1

feet

\newline

(B)

3

feet

\newline

(C)

9

feet

\newline

(D)

27

feet

Understand the problem: Understand the problem. $\newline$ We need to find the length of the space for each student, given that the total area is $756$ square feet and it fits $28$ students. Each student's space is $x$ feet wide and $3$ times as long.
Calculate area per student: Calculate the area for each student. $\newline$ Since the total area is $756$ square feet and there are $28$ students, we divide the total area by the number of students to find the area per student. $\newline$ Area per student = $\frac{\text{Total area}}{\text{Number of students}}$ $\newline$ Area per student = $\frac{756 \text{ square feet}}{28 \text{ students}}$
Perform division: Perform the division to find the area per student. $\newline$ Area per student = $\frac{756}{28}$ $\newline$ Area per student = $27$ square feet
Set up equation: Set up the equation for the area of each student's space. $\newline$ We know that the width is $x$ feet and the length is $3$ times the width. So, the area of each student's space is $x \times (3x)$ . $\newline$ Area per student = $x \times (3x)$ $\newline$ $27$ square feet = $x \times (3x)$
Solve for x: Solve for x. $\newline$ To find $x$ , we need to solve the equation $27 = 3x^2$ . $\newline$ Divide both sides by $3$ to simplify the equation. $\newline$ $\frac{27}{3} = \frac{3x^2}{3}$ $\newline$ $9 = x^2$
Find value of x: To find $x$ , we take the square root of both sides. $\newline$ $x = \sqrt{9}$ $\newline$ $x = 3$ feet
Determine length: Determine the length of each student's space. $\newline$ Since the length is $3$ times the width, we multiply $x$ by $3$ . $\newline$ Length $= 3 \times x$ $\newline$ Length $= 3 \times 3$ feet $\newline$ Length $= 9$ feet

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