Question 262227: In a group of 15,7 have studied Latin, 8 have studied Greek, and 3 have not studied either.How many of these studied both Latin and Greek
A.0 B.3 C.4 D.5
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website! First, draw a venn diagram with 2 circles. draw lines in each oval area and a line outside on the right side. These four lines need four numbers.
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step 1 - place "A" on the first line, "x" on the second line, "B" on the third line and "3" on the outside fourth line.
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step 2 - now we have some equations
(i) A + x + B + 3 = 15
(ii) A + x= 7
(iii) B + x = 8
adding (ii) and (iii), we get
(iv) A + B + 2x = 15
substituting (i) and (iv) we get
A + x + B + 3 = A + B + 2x
subtracting A and B we get
x + 3 = 2x
subtract x to get
x = 3.
3 studied both Latin and Greek
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