Proportion word problems

1. Cost of 5 pens is $25 and cost of 10 pencils is $50. What is more expensive?

 Solution. Ratios of number of pens and pencils whose cost is $25 and $50 respectively, is 

                                5 : 10 
                    5 :10 =  5/10  =  1/2

                 Ratio of their costs = 25 : 50
                     25 : 50 = 25/50 = 1/2

     Both the ratios 5 : 10 and 25: 50 are equal.
  Therefore, the cost of pens and pencils are equal.

 2. Cost of 4kg banana is $24 and cost of  5kg apple is $30. What is more expensive? 

Solution.  Ratios of weight of bananas and weight of apples 4kg and 5kg respectively, is 

                                4: 5 
                        4:5 =  4/5  = 4/5

                 Ratio of their costs = 24 : 30
                     24 : 30 = 24/30 = 4/5

       Both the ratios 4 : 5 and 24 : 30 are equal.

Therefore, the cost of bananas and apples are equal. 

3.  Sophia travels 60km in 2 hours and john travels 120km in 4 hours. Who travels faster?   

 Solution.  Ratio of distance traveled by sophia
                   and john is respectively, 

60 : 120  =  60/120  =  1/2

and ratio of time taken to cover these distance is

2 : 4  =  2/4  =  1/2

Both ratios are equal  60 : 120  =  2 : 4

Both traveled at same speed read as 60 is to 120 as 2 is to 4.