SOLVING PROPORTIONS WORD PROBLEMS
A proportion is an equation that states that two ratios or rates are equivalent.
Examples :
1/3 and 2/6 are equivalent ratios
1/3 = 2/6 is a proportion
We use cross product rule in proportion to solve many real world problems.
Let us consider the proportion
a : b = c : d
To know the cross product rule, first we have to know about extremes and means.
It has been explained in the picture given below.
Cross Product Rule :
Product of extremes = Product of means
ad = bc
Solving Proportions Word Problems - Examples
Example 1 :
Look at the picture below.
Janet drives from Clarkson to Humbolt in 2 hours. Suppose If she maintains the same driving rate, how many miles can she drive in 10 hours ?
Solution :
Given : Janet drives from Clarkson to Humbolt in 2 hours.
From the above information, we can get the following ratio between time and distance.
2 : 112 -----> (1)
Let "A" be the number of miles that she can drive in 10 hours.
Then, we have
10 : A -----> (2)
Since she maintains the same driving rate, the ratios (1) and (2) are equivalent.
So, we get the proportion
2 : 112 = 10 : A
Let us apply cross product rule
2A = 112 x 10
A = (112 x 10) / 2
A = 560
So, she can drive 560 miles in 10 hours.
Example 2 :
In 15 minutes, Lena can finish 2 math problems. At that rate, how many math problems can she finish in 75 minutes ? Use a double number line to find the answer.
Solution :
Given : Lena can finish 2 math problems in 15 minutes.
From the above information, we can get the following ratio between math problems and minutes.
2 : 15 -----> (1)
Let "B" be the number of math problems that she can finish in 75 minutes.
Then, we have
B : 75 -----> (2)
Since she maintains the same rate, the ratios (1) and (2) are equivalent.
So, we get the proportion
2 : 15 = B : 75
Let us apply cross product rule
2 x 75 = 15B
(2 x 75) / 15 = B
10 = B
So, Lena can finish 10 math problems in 75 minutes.
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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
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
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
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
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