Three rugs have a combined area of 200 sq meters. By overlapping the rugs to cover a floor area of 140 sq meters, the area covered by exactly two rugs is 24 sq meters. What area of the floor is covered by three rugs?Please explain your answer..... Show me how.....Thanks
Is this exactly how the problem is worded. or are you missing some details or making a typo (like the area of 2 rugs being 240 and not 24) ? what do you mean by combined. I assume, if you have 3 rugs with areas(R1, R2, R3) then I wonder if the combined area is R1+R2+R3 = 200 or R1R2R3=200 (since R1+R2 =24). when you say the area covered by exactly two rugs is 24 does this mean that the RUGs are separated. Do you want to know the area of the RUGs overlapped or separated.
First, the 140 sq meters of floor can be cateogrized into three categories: 1 - area covered by exactly one rug 2 - area covered by exactly two rugs 3 - area covered by exactly three rugs. If the combined area of the three rugs is 200 sq meters, and you are only covering 140 sq meters of floor, then 200 - 140 = 60 sq meters must be overlapped (meaning it is covered by either 2 or three rugs). Now since you say that 24 sq meters is covered by exactly two rugs, that means that the area covered by three rugs is 60 - 24 sq meters = 36 sq meters covered by three rugs. Hope this helps.
