Chase and his brother like to play basketball. About a month ago they decided to keep track of how many games they have each won. As of today, Chase has won 18 out of 30 games against his brother

How many games would Chase have to win in a row in order to have a 75% winning record? Chase would have to win games in a row to have a 75% winning record. How many games would Chase have to win in a row in order to have a 90% winning record? Chase would have to win games in a row to have a 90% winning record. Is Chase able to reach a 100% winning record? Chase (is or isn’t) able to reach a 100% winning record because .

Suppose that after reaching a winning record of 90 in part 2, Chase has a losing streak. How many games in a row would Chase have to lose in order to drop down to a winning record below 55% again?

Chase would have to lose games in order to drop down to a winning

Step-by-step explanation:

As of today, Chase has won 18 out of 30 games against his brother. The percentage of games that he has won as of today is

18/30 × 100 = 60%

In order to get 75% wins, let the number of games would be x. Then

(18 + x)/(30 + x) × 100 = 75

100(18 + x) = 75(30 + x)

1800 + 100x = 2250 + 75x

100x - 75x = 2250 - 1800

25x = 450

x = 450/25 = 18

chase has to win 18 games in a row.

In order to get 90% wins, let the number of games would be y. Then

(18 + x)/(30 + x) × 100 = 90

100(18 + x) = 90(30 + x)

1800 + 100x = 2700 + 75x

100x - 75x = 2700 - 1800

25x = 900

x = 900/25 = 36

chase has to win 36 games in a row in order to have a 90% winning record.

(18 + x)/(30 + x) × 100 = 100

100(1800 + x) = 100(30 + x)

1800 + 100x = 3000 + 100x

100x - 100x = 3000 - 1800

Therefore, it is impossible to for chase to reach a 100% winning record because he has already had some losses.

2) for a wining record of 90, the total number of games played is

30 + 36 = 66 games and the total number of wins was 18 + 36 = 54

In order to get 55% losses, let the number of games would be z. Then

(54 + z)/(66 + z) × 100 = 55

100(54 + z) = 55(66 + z)

5400 + 100z = 3630 + 55z

100z - 55z = 3630 - 5400

45z = - 1770

z = - 1770/45 = - 40

chase has to lose 40 games in a row in order to drop down to a winning record below 55% again.

10) (7k+6) (3k^2 +8)

11) (6x+7) (7x^2 - 6)

12) (p+6) (p^2 - 3)

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