SOLUTION: At a luncheon for 37 eminent people 25 requested for fried rice,15 requested for salad while 20 requested for shredded beef. 7 people requested for fried rice and salad,13 people r

Question 1185413: At a luncheon for 37 eminent people 25 requested for fried rice,15 requested for salad while 20 requested for shredded beef. 7 people requested for fried rice and salad,13 people requested for fried rice and shredded beef, and 8 people requested for salad and shredded beef, also 10 people requested for fried rice only, 5 people requested for salad only, find the number of people that requested for two different dishes
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52898)   (Show Source): You can put this solution on YOUR website!
.

            Was solved at this forum several months ago under this link

https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1172823.html

https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1172823.html

                       E N J O Y ( ! )

Answer by greenestamps(13214)   (Show Source): You can put this solution on YOUR website!

Let x be the number who requested all three items.

Since 7 ordered fried rice and salad, the number who ordered fried rice and salad but not shredded beef was 7-x; similarly, since 8 ordered shredded beef and salad, the number who ordered salad and shredded beef but not fried rice was 8-x.

And 5 people ordered salad only.

Then the total number who ordered salad was x (all three items), plus (7-x) (fried rice and salad), plus (8-x) (salad and shredded beef), plus 5 (salad only).

But the total number who ordered salad was 15:

Now you have all the information you need to get the answer.

fried rice and salad only: 7-x = 7-5 = 2
salad and shredded beef only: 8-x = 8-5 = 3
fried rice and shredded beef only: 13-x = 8

Total who ordered two different dishes: 2+3+8 = 13.

ANSWER: 13

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