Arectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. if regular tiles cover 80 square feet of the wall, and no tiles overlap, what is the area of the entire wall? a. 160b. 240c. 360d. 440e. 560

D. 440

Explanation:

Let's call R the number of regular tiles on the wall, J the number of Jumbo tiles on the wall, T the number of tiles on the wall, Ar the area of every regular tile and Aj the area of every Jumbo tile.

Then, the equation that describe the area of the entire wall is:

A = (R*Ar) + (J*Aj)

Where (R*Ar) is the are that is cover by regular tiles and (J*Aj) is the area that is cover by Jumbo tiles.

From the question we know that regular tiles cover 80 square feet of the wall, so:

R*Ar = 80

On the other hand, 1/3 of the tiles are jumbo tiles, so:

(1/3)T = J

T = 3J

Additionally, the sum of regular tiles and Jumbo tiles give as the number of tiles on the wall, then we can formulate the following equation:

R + J = T

R + J = 3J

R = 3J - J

R = 2J

R/2 = J

We also know that Jumbo tiles have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles, so if we call L the length of the regular tiles and W the width of the regular tiles, we have:

Ar = LW

Then, the area of the Jumbo tiles is:

Aj = (3L)*(3W) = 9LW

Aj = 9Ar

If we replace the equation R/2 = J and Aj = 9Ar on the initial equation we get:

A = (R*Ar) + (J*Aj)

Finally, replacing R*Ar by 80, we get:

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