Question

a rectangular meeting - room has a raised platform that is the same length as the room. the whole room has an area of 46 14/15 square yards. the length of the room is 7 1/3 yards. part a what is the width of the room excluding the raised platform, in yards? leave your answer as an improper fraction. 1) find the total width by dividing the area by the length. simplify completely!!! 2) subtract the total width minus the raised - platform width. part b what fraction of the entire floor is the raised platform? a) 1/15 b) 1/8 c) 1/6 d) 1/3

Explanation:

Part A

Step1: Convert mixed - numbers to improper fractions

The area of the room is $46\frac{14}{15}=\frac{46\times15 + 14}{15}=\frac{690+14}{15}=\frac{704}{15}$ square yards, and the length is $71\frac{1}{3}=\frac{71\times3+1}{3}=\frac{213 + 1}{3}=\frac{214}{3}$ yards.

Step2: Calculate the total width

The total width $w_{total}=\frac{704}{15}\div\frac{214}{3}=\frac{704}{15}\times\frac{3}{214}=\frac{704\times3}{15\times214}=\frac{2112}{3210}=\frac{11}{15}$ yards.

Part B

Let's assume the area of the raised - platform is $A_{platform}$ and the area of the whole floor is $A_{total}=46\frac{14}{15}=\frac{704}{15}$ square yards. If we assume the length of the platform is the same as the room length $l = 71\frac{1}{3}=\frac{214}{3}$ yards and width of the platform is $1$ yard, then $A_{platform}=\frac{214}{3}\times1=\frac{214}{3}$ square yards. The fraction of the raised platform to the entire floor is $\frac{\frac{214}{3}}{\frac{704}{15}}=\frac{214}{3}\times\frac{15}{704}=\frac{214\times15}{3\times704}=\frac{1}{15}$.

Answer:

Part A

$\frac{11}{15}$

Part B

A. $\frac{1}{15}$