pzazz12 wrote:Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?
A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters
This problem is testing your knowledge of overlapping groups. Here is the formula for 3 overlapping groups in which sometimes 2 groups overlap and sometimes all 3 groups overlap:
T = G1 + G2 + G3 - (those in 2 of the groups) - 2*(those in all 3 groups)
When we count everyone in the 3 groups, those in 2 of the groups will be counted twice, so they need to subtracted from the total
once. Those in all 3 groups will be counted 3 times, so they need to be subtracted from the total
twice.
In the problem above:
T = the area of the room = 140
G1+G2+G3 = combined area of the 3 rugs = 200
Those in 2 of the groups = area covered by 2 of the rugs = 24
Let x = those in all 3 groups = area covered by all 3 rugs
Plugging into the formula, we get:
140 = 200 - 24 - 2x
-36 = -2*x
x = -36/-2 = 18.
The correct answer is A.
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