Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 15, 2023

Find equation for total cost $y$ of tile backsplash with installation fee $\$ 150$ and tile price $\$ 2.75$ per square foot $x$ .

STEP 1

Assumptions
1. The installation fee is a fixed cost of $150.<br />2. The tile cost is variable and depends on the area in square feet, denoted by$ x $.<br />3. The tile cost per square foot is$ 2.75.
4. The total cost, denoted by $y$ , is the sum of the installation fee and the cost of the tile based on the area.

STEP 2

The total cost of the backsplash, $y$ , can be represented as the sum of the fixed installation fee and the variable cost of the tile.
$y = \text{Installation fee} + (\text{Cost per square foot} \times \text{Area in square feet})$

STEP 3

Now, plug in the given values for the installation fee and the cost per square foot into the equation.
$y = \$150 + (\$2.75 \times x)$

STEP 4

This equation represents the total cost, $y$ , as a function of the area in square feet, $x$ .
The equation that best represents the total cost, $y$ , of the backsplash is:
$y = 150 + 2.75x$

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