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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

#1
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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.

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Feb 2, 2021