Question

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.

Answer 1

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

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
`= 3* n =3n`

and points earned by his little brother in n successful flip
`= 1* n=n`.

Total points of Chase
`= 19+3n\cdots(i)`

Total points of his little brother
`= 27 + n\cdots(ii)`

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

`19+3n = 27 + n \\\\\Rightarrow 3n-n = 27-19 \\\\\Rightarrow 2n=8 \\\\\Rightarrow n=8/2=4`

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
`= 19+ 3* 4 = 31.`

Hence, each brother has 31 points.