In a rock-paper-scissors game, a winner gets 5 points and a loser gets 2 points. after a man played this game 20 times, his total score was 67 points. how many times did he win, and how many times did he lose

The man wins 9 times and looses 11 times in the rock - paper-scissor game.

Step-by-step explanation:

Let us assume that in the game:

Number of times  man wins the games = x times

Number of times  man loses the games = y times

Total number of attempts = 20

Points after winning = 5

Points after loosing = 2

Now, according to the question:

       x  + y =20

and 5 x + 2 y = 67

Now, from (1) y = 20-x,     put in (2)

5x + 2y = 67       ⇒           5x + 2(20 -x)  = 67

or, 5x -2x = 67 - 40

or, 3x = 27

⇒ x = 27/3 = 9

then y = 20 - x = 20 - 9 = 11

⇒ x = 9 and y = 11 is the solution of the given system.

Hence, the man wins 9 times and looses 11 times in the rock - paper-scissor game.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for