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The Phillies won 3 of their first 21 games. How many games in a row after these 21 games do the Phillies have to win in order to have won exactly 3/5 of the games they have played? Please help I do not understand the question

 Feb 2, 2021
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The Phillies won 3 of their first 21 games. How many games in a row after these 21 games do the Phillies have to win in order to have won exactly 3/5 of the games they have played? Please help I do not understand the question     

 

Let X represent the number of new games they must win to attain a 3/5 win/loss ratio.  3/5 can also be written 60%.

 

 3           X + 3  

––   =   ––––––  

 5          X + 21  

 

Cross multiply to get                3 • (X + 21)  =  5 • (X + 3)  

 

Multiply                                          3X + 63  =  5X + 15  

 

Subtract 3X from both sides                  63  =  2X + 15  

 

Subtract 15 from both sides                  48  =  2X  

 

Divide both sides by 2                             X  =  24    

 

If the Phillies win their next 24 games they will have an overall win/loss ratio of 3/5 or 60%.  

 

Check the figures:   3 + 24 wins out of a total 21 + 24 games ..... so 27/45 reduces to 3/5. 

.

 Feb 2, 2021

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