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There were 217 more visitors on Sunday than on Monday at an art exhibition. 4/7 of the visitors on Sunday and 3/4 of the visitors on Monday were men. 302 women visited on both days altogether. Find the total number of visitors on both days.

Source: my pal


Given the denominators 7 and 4, we might try working with 7x4 = 28 units.

Let Monday's visitor = 28u.
So Sunday's visitor  = 28u + 217.
1/4 of Monday's visitors are women = 1/4 x 28u         = 7u
3/7 of Sunday's visitors are women = 3/7 x (28u + 217) = 12u + 93
Total number of women = 19u + 93 = 302.
So u = (302 - 93)/19 = 11.

So Monday's total is 28x11 = 308.
Sunday's total is 308 + 217 = 525.
Total visitors on both days is 308 + 525 = 833.
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I think between @sushi88’s and your answer, yours is a bit easier to understand, whilst @sushi88’s require a little more visualizing.  Regardless, I think this problem sum is ridiculously convoluted and twisted.  Maybe I’ll try using equations later 🙂

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Chief, visualization means to form a picture of someone or something in your mind, in order to imagine.  Mine needs no visualization, it is crystal clear to the eyes.  WYSIWYG(What you see is what you get)  is how I presented the info into a tabular form with no imagination required of the fractions; as-is…idea is to form the one-variable equation.

After forming the equation, the rest is just mathematical skills in massaging the equation.

This question is not considered convoluted, there are definitely worse ones…LOL.  It is trying to give a lot of information and the skill involved is to ORGANISE the information so that it can be easily solved, hence the tabular information is one of the ways I used….like what a CEO would like to look at too. kekeke


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Yes,  visualization is not the right word.  I know you mainly interpreted what you read from the text,  but the problem gets confusing.

Oh well… just happy my psles are over… 🙂

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                            Total Visitors             Men                       Women

Sunday                 u+217                  (4/7)(u+217)                (3/7)(u+217)                

Monday                    u                            (3/4)u                      (1/4)u

Total women given is 302

(3/7)(u+217) + (1/4)u = 302           (Multiply both sides by 28)

12u + 2604 + 7u = 8456

19u =5852

u = 5852/19 = 308

Visitors on Sunday = 308+217 = 525

Visitors on Monday = 308

Total visitors on both days = 525 + 308 = 833 


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