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# AV- Question 24 Carpet lnstallation

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### AV- Question 24 Carpet lnstallation - Page Text Content

FC: Question 24 Carpet Installation by Anna Vaughan

1: Question 24: A room 8 meters by 6 meters is to have a carpet installed in one corner, leaving a strip of floor x meters wide around the other two sides. >Write an expression for the length and for the width of the carpet in terms of x. >Write an expression for the area of the carpet in terms of x. >Write an inequality stating that the area of the carpet is at least 70% of the area of the room. Solve the inequality to find the possible values of x. Support your answer. >What values of x make the carpet no more than half the area of the room? Explain.

2: Write an expression for the length and for the width of the carpet in terms of x. | The length of the carpet in terms of x is 8-x | The width of the carpet in terms of x is 6-x

3: Write an expression for the area of the carpet in terms of x. | In terms of x, the area of the carpet is (8-x)(6-x)

4: Write an inequality stating that the area of the carpet is at least 70% of the area of the room. Solve the inequality to find the possible values of x. Support your answer. | (8-x)(6-x)>48(.7) | First it is necessary to simplify this inequality. x^2-14x+48 > 33.6 x^2-14x+14.4> 0 Next, put this inequality into your calculator and evaluate the possible values of x. | The possible values of x are any values greater than or equal to 1.4. This shows that 'x' amount of the floor must be carpet.

5: What values of x make the carpet no more than half of the area of the room? Explain. | The values of x that make the carpet no more than half the area of the room would be greater than 0 and less than or equal to 2.

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• By: Anna V.
• Joined: almost 8 years ago
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