[size=12.0012px]A rectangular 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?
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The length and the width of a regular tile can be represented as L and w. The length of a jumbo tile, then, is 3L. If the ratio of length to width is the same for all tiles, and the ratio of the regular tile is L : w then a jumbo tile must have a width of 3w.
Represent the area of both types:
Area of one regular tile = Lw
Area of one jumbo tile = (3L)(3w) = 9Lw
If 1/3 of the tiles are jumbo, then the other 2/3 must be regular (since only two kinds of tiles are used). There are twice as many regular tiles as jumbo ones. If J is the number of jumbo tiles, then there are 2J regular tiles.
Area of all jumbo tiles = (the area of one jumbo tile)(the number of jumbo tiles)
Area of all jumbo tiles = (9Lw)(J)
Area of all regular tiles = (the area of one regular tile)(the number of regular tiles)
Area of all regular tiles = (Lw)(2J) = 80
Remember that the problem tells you that the area of all regular tiles is 80! Solve to find the value of LwJ:
(Lw)(2J) = 80
LwJ = 40
Find the area of jumbo tiles:
Area of all jumbo tiles = (9Lw)(J)
Area of all jumbo tiles = (9)(40) = 360
Add them up! Regular + jumbo is 80 + 360, or 440.
Alternatively, use a neat shortcut. If 1/3 of the tiles are jumbo, then 2/3 are regular. In that case, for every two regular tiles, there is one jumbo tile. One jumbo tile has an area 9Lw and two normal tiles have an area 2Lw, so the tiles will be placed in "sets" of 9Lw + 2Lw = 11Lw. The correct answer, then, must be a multiple of 11, and only answer (D) is a multiple of 11.
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发表于 2017-5-30 23:18:29
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