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AQA maths non calculator

females are two times the amount of males in a office
1/4 of females wear glasses
3/8 of males wear glasses
84 people wear glasses overall
how many people in the office?

how do you answer this??????
First you multiply 1/4 by 2/3 (as two parts of the office are females) (1/4 x 2/3 = 2/12 = 1/6)From this you get 2/12 or 1/6Then you do the same thing for the men and multiply 3/8 by 1/3 (as 1 part of the office are males) (3/8 x 1/3 = 3/24 = 1/8)From this you get 3/24 or 1/8Then you add 1/8 to 1/6 (3/24 4/24 = 7/24)This gives you 7/24 which is the total fraction of people in the office which wear glassesTherefore 7/24=84So to find one part you divide 84 by 7 which gives you 12 (84/7 = 12)One part = 12Finally you multiply 12 by 24 to get the total amount of people in the office (24 x 12 = 288)So the total amount of people in the office is 288To check your answer you divide 288 by 3 which gives you 96 (288/3 = 96)Then you multiply 96 (which is 1/3 of the office) by 3/8 (this tells you how many men wear glasses) which gives you 36 (3/8 x 96 = 36)Then you multiply 96 by 2 (which is 2/3 of the office) and multiply that by 1/4 (which gives you how many females in the office wear glasses) which gives you 48 (96 x 2 = 192 then 192 x 1/4 = 48)Then you add 36 (total men wearing glasses) to 48 (total women wearing glasses) (36 48 = 84)
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