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Answer :
Sure! Let's work through the problem step-by-step.
(a) Determine a linear function that predicts the cost y (in dollars) to carpet an x-square foot office.
The problem states that there is a fixed installation cost of [tex]$100, and an additional cost of $[/tex]12 per square foot for the carpeting. To write a linear function for the total cost [tex]\( y \)[/tex], we can use the formula:
[tex]\[ y = \text{fixed cost} + \text{(cost per square foot)} \times x \][/tex]
Substituting the given values:
[tex]\[ y = 100 + 12x \][/tex]
So the linear function is [tex]\( y = 100 + 12x \)[/tex].
(b) Use this function to determine the cost (in dollars) to carpet 297 square feet of floor space.
Now that we have the function [tex]\( y = 100 + 12x \)[/tex], we can find the cost for 297 square feet by substituting [tex]\( x = 297 \)[/tex] into the equation:
[tex]\[ y = 100 + 12(297) \][/tex]
First, calculate the product:
[tex]\[ 12 \times 297 = 3564 \][/tex]
Then, add the fixed cost:
[tex]\[ y = 100 + 3564 = 3664 \][/tex]
Therefore, the cost to carpet 297 square feet of floor space is [tex]\( \$3664 \)[/tex].
(a) Determine a linear function that predicts the cost y (in dollars) to carpet an x-square foot office.
The problem states that there is a fixed installation cost of [tex]$100, and an additional cost of $[/tex]12 per square foot for the carpeting. To write a linear function for the total cost [tex]\( y \)[/tex], we can use the formula:
[tex]\[ y = \text{fixed cost} + \text{(cost per square foot)} \times x \][/tex]
Substituting the given values:
[tex]\[ y = 100 + 12x \][/tex]
So the linear function is [tex]\( y = 100 + 12x \)[/tex].
(b) Use this function to determine the cost (in dollars) to carpet 297 square feet of floor space.
Now that we have the function [tex]\( y = 100 + 12x \)[/tex], we can find the cost for 297 square feet by substituting [tex]\( x = 297 \)[/tex] into the equation:
[tex]\[ y = 100 + 12(297) \][/tex]
First, calculate the product:
[tex]\[ 12 \times 297 = 3564 \][/tex]
Then, add the fixed cost:
[tex]\[ y = 100 + 3564 = 3664 \][/tex]
Therefore, the cost to carpet 297 square feet of floor space is [tex]\( \$3664 \)[/tex].
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