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Answer:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4,
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.
The way we can find out the unit rate (also known as the <em><u>SLOPE</u></em>) is by using the table as coordinates!
The slope formula is
With the table, the TIME column can be "x"
The DISTANCE column can be "y"
____________________________
As coordinates, it would look like...
(0,0)
(20, 25)
(30, 37.5) and so on!
_____________________________
All we need to do now is use 2 of these coordinates and plug them into the slope formula in their correct places to find the unit rate!
Example:
solve!
= 12.5/10 ⇒ 1.25 ( or 5/4 in fraction form)