A wall's height is two-thirds that of its length. The entire...

A wall's height is two-thirds that of its length. The entire wall will be painted. The paint costs $\$ 12$ per gallon, and 1 gallon of paint covers 60 square feet. What expression gives the cost of the paint (assuming one can purchase partial and full gallons) to cover a wall that is $\mathrm{L}$ feet long? (A) $\quad$ Cost $=L^{2}$ (B) $\quad$ Cost $=\frac{1}{5} L^{2}$ (C) $\quad$ Cost $=\frac{2}{15} L^{2}$ (D) $\quad$ Cost $=\frac{3}{64} L^{2}$

A wall's height is two-thirds that of its length. The entire wall will be painted. The paint costs $\$ 12$ per gallon, and 1 gallon of paint covers 60 square feet. What expression gives the cost of the paint (assuming one can purchase partial and full gallons) to cover a wall that is $\mathrm{L}$ feet long?
(A) $\quad$ Cost $=L^{2}$
(B) $\quad$ Cost $=\frac{1}{5} L^{2}$
(C) $\quad$ Cost $=\frac{2}{15} L^{2}$
(D) $\quad$ Cost $=\frac{3}{64} L^{2}$

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Key Concepts

Algebraic Expression Formulation

This concept involves assembling various elements of a problem into a single algebraic expression. It requires combining computed values, such as area and cost per unit, to create a model that accurately represents the situation and facilitates further analysis.

Unit Conversions in Application Problems

Unit conversion is crucial when dealing with measurements in different units. In applications such as painting, it involves converting the calculated area (in square feet) into the amount of material required (in gallons), using predetermined coverage rates.

Area Calculation of Rectangular Shapes

Calculating the area is fundamental when determining the amount of material needed to cover a surface. For rectangular shapes, the area is determined by multiplying the length by the height, forming the basis of many applied geometry problems.

Ratios and Proportions

This concept explains how two quantities relate through a constant ratio. In many mathematical problems, especially in geometry and algebra, ratios help determine one dimension from another, establishing a direct relationship between different measures.

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