math problem

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Ca'i pho`ng cu?a tui co' 50 ca'i ma'y computer, 20 ca'i co' the^? cha.y win os, 10 ca'i co' the^? cha.y linux os, 5 ca'i co' the^? cha.y mac os, va` so^' co`n la.i co' the^? cha.y unix os. Trong so^' 50 ca'i ma'y ddo' thi` 5 ca'i co' the^? cha.y ddu+o+.c win & linux os, 3 ca'i cha.y ddu+o+.c linux & mac os,2 ca'i cha.y ddu+o+.c win & mac os, va` 9 ca'i cha.y ddu+o+.c ca? win, linux, & mac os. Dzi. la`m sao mi`nh bie^'t ddu+o+.c co' bao nhie^u ca'i ma'y trong pho`ng chi? cha.y ddu+o+.c unix os tho^i ?

[Trung Quốc]

begin to draw overlap circles and fill in the info.

you have 3 circles represent for W, L, and M. These 3 cirlce will be overlap each other. There are 9 computer can run under W, L and M so put 9 in the place where 3 circle overlap. There are 5 can run W and L so put 5 in the place where the W circle and L cirlce overlap. There are 3 running L and M so put 3 in the place where L circle and M cirlce overlap. There are 2 that can run W and M so put 2 in the place where W circle and M circle overlap.

1) Now use your hand to cover the M and L circle, leave the one that overlap with the W circle there, don't cover it. Now you should see the W cirlce have 4 sections, 3 of them fill up with 2, 9 and 5, the other one is not. However from the info we know that there are 20 comp can run W so we take 20- 2 - 9 - 5 we should get the number of computer that only run W.
2) Repeat step 1 for both M and L circle then you should be able to figure all of them.

If you want to check your answer, you can post it here, I will tell you if you did it correct or not.


QT

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W only = 20 - ( 9 + 5 + 2 ) => hi`nh nhu+ ho^ng ddu'ng ta.i dzi` 9 ma'y WLM la^'y trong so^' ma'y cu?a WL, LM, & MW.

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ca'ch cu?a tui:

(20 + 10 + 5 ) = 35 ca'i ma'y cha.y win or linux or mac nhu+ng no' la` over count ru`i. Ba^y gio+` mi`nh ti`m so^' lu+o+.ng ma'y bi. ti'nh nhie^`u ho+n 1 la^`n ddo':

9 ma'y cha.y ddu+o+.c win & linux & mac os ( 9 ma'y na`y kho^ng bi. over count ) thi` cu~ng co' the^? cha.y ddu+o+.c win & linux or linux & mac or mac & linux os. Nhu+ng 9 kho^ng chia he^'t cho 10 ( 5 + 3 + 2 ma'y co' the^? cha.y 2 os ) => chi? co' 1 ma'y chi? cha.y ddu+o+.c 2 thu+' tho^i va` la` ca'i ma'y bi. over count ( thi' du. co' 1 ma'y cha.y ddu+o+.c 2 thu+' win & linux, thi` khi bi. ho?i co' bao nhie^u ma'y co' the^? cha.y win bao nhie^u ma'y co' the^? cha.y linux thi` ca^u tra? lo+`i la` co' 1 ma'y co' the^? cha.y win va` 1 ma'y co' the^? cha.y linux nhu+ng thie^.t ra no' chi? la` 1 ma'y cha.y ddu+o+.c 2 thu+' ).

35 - 1 = 34 ca'i ma'y kho^ng cha.y unix os

=> 50 - 34 = 16 so^' ma'y cha.y unix os

[Trung Quốc]

oh, man, I didn't check it last night but the logic in this problem failed:

"10 ca'i co' the^? cha.y linux os, 5 ca'i co' the^? cha.y mac os," this one tell us that there are only 10 computer can run linux. However there are 9 of them can run WML and, so we know that there are at least 9 computer can run L from that statement. Another statement is that there are 5 computer can run WL so we know another 5 can furn Linux, now the total is 14 + another 2 from ML so there are 16 can run L.

It is the same way for M computer. :)

Either that or miss-communication :)

Or I need to get some sleep. :D

"thi` cu~ng co' the^? cha.y ddu+o+.c win & linux or linux & mac or mac & linux os." maybe I am not understand your problem correctly, but if the computer count as it can run under WML then I wouldn't count it again for the WM or WL or ML unless I am miss translate it. :D

Could you please post the problem exactly as it is word in English? (I hope. :))

QT

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"thi` cu~ng co' the^? cha.y ddu+o+.c win & linux or linux & mac or mac & linux os."

co' 3 chu+~ ABC thi` co' bao nhie^u ca(.p (2) chu+~ ddu+o+.c ta'ch ra ( AB == BA ) => AB, AC, BC

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ba`i na`y co' va^'n dde^` ru`i:

9 ca'i co' the^? cha.y WLM ma` chi? co' 5 ca'i co' the^? cha.y WL ?

cha('c ba`i na`y cha('c no' no'i la` 5 ca'i chi? cha.y WL, 3 ca'i chi? cha.y LM, 2 ca'i chi? cha.y MW, va` 9 ca'i chi? cha.y WLM. Ne^'u dzi. thi` cu~ng ho^ng ddu'ng, 50 - ( 20 + 10 + 5 + 5 + 3 + 2 + 9 ) = dda'p so^' => dda'p so^' la` negative ?


ba`i na`y tui chi? co' ba?n tie^'ng vie^.t tho^i.

[Trung Quốc]

boi vay. :)

QT

[yeudoi]

Unix system only ?

Có thể run Unix = 50 - (20 Wins + 10 Lin +5 Mac ) = 15 cái

Dual boots
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5 cái Linux and Wins
3 cái Linux and Mac
2 cái Win + Mac
9 cái Win + Linux + Mac


5 cái ''có thể'' chạy Mac? lol... Wording problem here... From the information given we can see that we can have at least 14 Macs

10 cái "có thể " Linux? Man... 9 + 3 + 5 = 17 here, we can have at least 17 Linux here?