Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Chase and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Chase starts with 19 points, and his little brother starts with 27 points. Chase gets 3 points for every successful shot, and his brother, since he is younger, gets 1 point for each successful shot. Eventually, the brothers will have a tied score in the game. How many points will they both have? How many additional shots will each brother have made? Chase and his brother will both have a score of by making shots.

Chase and his brother will both have a score of 31 points by making 4 successful shots.

Step-by-step explanation:

Given that initially Chase has 19 points and his brother has 27 points.

In one successful flip, Chase get 3 points and in one successful flip, his little brother get 3 points

Assuming that both have the same score after n number successful flip of the coin.

So, points earned by Chase in n successful flip

and points earned by his little brother in n successful flip .

Total points of Chase

Total points of his little brother

As the brothers have tied scores in the game, that means both have the same score, so from equations (i) and (ii), we have

So, after n successful throw, both have the same score.

Hence, each brother made 4 additional successful shots.

Now, put n=4 inequation (i) or (ii) to get the total points, i.e

Total points of each brother

Hence, each brother has 31 points.