SOLVING WORD PROBLEMS INVOLVING SETS
Problem 1 :
There are 40 students in a class. 20 take Chemistry and 25 take French. 8 students take both.
(i) Find how many students take none.
(ii) How many are there in at least one classes?
Solution :
Total number of students = 40
Let A and B be the students who took Chemistry and French respectively.
n(A) = 20, n(B) = 25 and n(AnB) = 8
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) = 20 + 25 - 8
= 45 - 8
n(AUB) = 37
Number of students who take none = Total number of students - Number of students who take one
= 40 - 37
= 3
So, the number of students who take none is 3 and number of students are in atleast one class is 37.
Problem 2 :
A group of 20 college students were asked whether they are using the social net working sites. For that 8 said they use face book. 10 said they use twitter. 4 said they use both.
(i) Find how many are not using none?
(ii) Find how many are using only face book and twitter?
Solution :
Let A and B be the students who uses Face book and twitter respectively.
Number of students = 20
n(A) = 8, n(B) = 10, n(A n B) = 4
(i) To find the number of students who are not using any of these, we have to subtract number of students who uses one from the total number of students.
n(A U B) = n(A) + n(B) - n(A n B)
= 8 + 10 - 4
= 14
Number of students who use none = 20 - 14
= 6
Number of students who use face book = n(A) - n(A n B)
= 8 - 4
= 4
Number of students who use twitter = n(B) - n(A n B)
= 10 - 4
= 6
Problem 3 :
At a breakfast buffet, 20 people chose coffee and 17 chose juice. 10 people chose both coffee and juice. If each person chose at least one of these beverages, how many people visited the buffet?
Solution :
Let A and B be the students who choose coffee and juice respectively.
n(A) = 20, n(B) = 17, n(AnB) = 10
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) = 20 + 17 - 10
= 37 - 10
n(AUB) = 27
So, the number of people who visited the buffet is 27.
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
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Complementary and supplementary angles word problems
Trigonometry word problems
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Word problems on sets and venn diagrams
Pythagorean theorem word problems
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Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
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Sum of all three four digit numbers formed with non zero digits
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