Question

Jacob and his brother like to play basketball. About a month ago they decided to keep track of how many games against his brother. Jacob has won 25 out of the 60 games against his brotherA. How many games would Jacob have to win in a row in order to have 75% winning record?B. How many games would Iacob have to win in a row in order to have 90% winning record?C. Is Jacob able to reach a 100% winning record? Explain why or why not.D. Suppose that after reaching a winning record of 90% in part (b), Jacob had a losing streak. How many games in a row would Jacob have to lose in order to drop down to a winning record below 45% again.

Answer 1

A. Let's call

x: number of games in a row, won by Jacob

If Jacob won the next x games, his record would be 75% if:

(25 + x)/(60 + x) = 0.75

Solving for x:

25 + x = 0.75*(60 + x)

25 + x = 45 + 0.75x

x - 0.75x = 45 - 25

0.25x = 20

x = 20/0.25

x = 80

B. Similar than the previous item:

(25 + x)/(60 + x) = 0.9

25 + x = 0.9*(60 + x)

25 + x = 54 + 0.9x

x - 0.9x = 54-25

0.1x = 29

x = 29/0.1

x = 290

C. He is not able to reach a 100% winning record because he already lost 35 games

D. Games won by Jacob: 25 + 290 = 315

Total games played: 60 + 290 = 350

If Jacon lose y games in a row, his record will be:

315/(350 + y)

We want that record below 45%, then:

315/(350 + y) < 0.45

Solving for y:

315 < 0.45*(350 + y)

315 < 157.5 + 0.45y

315 - 157.5 < 0.45y

157.5/0.45 < y

350 < y

They have to play more than 350 new games