Unit rates :
When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates.
Example 1 :
Cost of a dozen pens is $180 and cost of 8 ball pens is $56. Find the ratio of the cost of a pen to the cost of a ball pen.
To find the ratio of the cost of a pen to the cost of the ball pen, we have to find the unit rate.
Cost of 12 pens = $180
Cost of one pen = 180/12 ==> 15
Cost of 8 ball pens = $56
Cost of one ball pen = 56/8 ==> 7
Cost of a pen : Cost of a ball pen = 15 : 7
Example 2 :
Divide 20 pens between Mary and John in the ratio of 3 : 2.
Number of pens got by Mary = 3x
Number of pens got by John = 2x
To find number of pen got by Mary and John respectively, we have to find the unit rate.
3x + 2x = 20
5x = 20
x = 20/5 ==> 4
3x = 3(4) = 12
5x = 5(4) = 20
Hence Mary will get 12 pens and John will get 20 pens.
Example 3 :
Mother wants to divide $36 between her sons Daniel and David in the ratio of their ages. If age of Daniel is 15 years and age of David is 12 years,find how much Daniel and David will get.
Ratio of the ages of Daniel and David = 15 : 12
15x, 12x be the amount got by Daniel and David respectively.
15x + 12x = 36
17x = 36
x = 36/17 ==> 1.33
15x = 15(1.3) ==> 19.95 ==> 20 (Approximately)
12x = 12(1.3) ==> 15.96 ==> 16 (Approximately)
Hence the amount got by Daniel and David are $20 and $16 respectively.
Example 4 :
The length and breadth of a rectangle are in the ratio 4:7. If the breadth is 77 cm, find the length?
Breadth = 77 cm
The ratio of length to breadth is 4 : 7
Breadth = 7 parts
7 parts = 77 cm
1 part = 77/7 = 11 cm
length = 4 parts
4 parts = 4 x 11 cm = 44 cm
Length of the rectangle = 44 cm.
Example 5 :
In a village of 1,21,000 people, the ratio of men to women is 6 : 5 Find the number of men and women?
Number of people in the village = 1,21,000
Ratio of men to women = 6 : 5
Total number of parts = 6 + 5 = 11
11 parts = 1,21,000
1 part = 1,21,000/11 ==> 11,000
Number of men in the village = 6 x 11,000 = 66,000
Number of women in the village = 5 x 11,000 = 55,000
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