# PROPORTION 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 Proportion Word Problems - Examples

Example 1 :

If you can buy one can of pineapple chunks for \$2 then how many can you buy with \$10 ?

Solution :

From the given information, number of cans of pineapple chunks and the cost are in the ratio

1 : 2

Let 'x' be the number of cans that we buy.

Then,

1 : 2  =  x : 10

1(10)  =  2x

10  =  2x

5  =  x

So, we can buy 5 apples with \$10.

Example 2 :

Shawna reduced the size of a rectangle to a height of 2 in. What is the new width, if it was originally 24 in wide and 12 in tall ?

Solution :

From the given information, the width and height  of the rectangle are in the ratio

24 : 12  =  2 : 1

Because the original width and height of the rectangle are in the ratio 2 : 1, the width and height of he resized rectangle will also be in the same ratio.

And also, the height of the rectangle is reduced to 2 inches.

Let 'x' be the width of the resized rectangle.

Then,

2 : 1  =  x : 2

2(2)  =  1(x)

4  =  x

So, the width of the resized rectangle is 4 inches.

Example  3 :

One cantaloupe costs \$2. How many cantaloupes can we buy for \$6 ?

Solution :

From the given information, number of cans of pineapple chunks and the cost are in the ratio

1 : 2

Let 'x' be the number of cantaloupe that we buy.

Then,

1 : 2  =  x : 6

1(6)  =  2(x)

6  =  2x

3  =  x

So, we can buy 3 cantaloupes for \$6.

Example 4 :

Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for \$2. How many Tala would she get if she exchanged \$6?

Solution :

From the given information, the exchange rate of Tala and Dollar are in the ratio

6 : 2  =  3 : 1

Let 'x' be the number of Tala that Ming would expect.

Then,

3 : 1  =  x : 6

3(6) = 1(x)

18  =  x

So, Ming would get 18 Tala, if she exchanged \$6.

Example 5 :

Jasmine bought 32 kiwi fruit for \$16. How many kiwi she Lisa buy, if she has \$4 ?

Solution :

From the given information, we come to know that number of kiwi fruits to the cost is in the ratio

32 : 16  =  2 : 1

Let 'x' be the number of kiwi that jasmine buy for \$4.

2 : 1  =  x : 4

2(4)  =  1(x)

8  =  x

So, Jasmine can buy 8 kiwi fruits for \$4.

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Decimal representation of rational numbers

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L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

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