**Using proportion to solve 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

**Example 1 :**

The distance Ali runs in 40 minutes is 3 miles. At this rate, how far can he run in 60 minutes ?

**Solution :**

Let "A" be the number of miles that he can run in 60 minutes.

From the given information, we can write the following proportion.

In the proportion

40 : 3 = 60 : A

the extremes are 40 & A and means are 3 & 60.

Let us apply cross product rule.

40A = 3 x 60

Dividing by 40 on both sides, we get

A = 180 / 40

A = 9/2 or 4 1/2

At this rate, Ali can run 9/2 miles, or 4 1/2 miles, in 60 minutes.

**Example 2 :**

Ms. Reynolds has a system of 10 sprinklers that water her entire lawn. The sprinklers run one at a time, and each runs for the same amount of time. The first 4 sprinklers run for a total of 50 minutes. How long does it take to water her entire lawn ?

**Solution :**

Let "T" be the time takes to water the entire lawn.

From the given information, we can write the following proportion.

In the proportion

50 : 4 = T : 10

the extremes are 50 & 10 and means are 4 & T.

Let us apply cross product rule.

50 x 10 = 4T

Dividing by 4 on both sides, we get

500 / 4 = T

125 = T

Hence, it takes 125 minutes or 2 hours 5 minutes to water her entire lawn.

After having gone through the stuff given above, we hope that the students would have understood "How to use proportion to solve problems".

Apart from the stuff given above, if you want to know more about "Using proportion to solve problems", please click here

Apart from the stuff given in this stuff, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM 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**

**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**