SOLVING PROPORTIONS WORD PROBLEMS
About "Solving proportions word problems"
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
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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