**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

**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

Hence, 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

Hence, Lena can finish 10 math problems in 75 minutes.

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