# 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

## 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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6